Pub Date : 2019-07-03DOI: 10.1080/1726037X.2019.1651492
A. Ehsani, F. Ghane
Abstract This paper concerns the chaos game of random iterated function systems. We consider a random iterated function system IFS() generated by a finite family of Lipschitz maps on a compact ball of ℝn with the weak average contraction condition and show that it admits a quasi-attractor satisfying the deterministic chaos game. In particular, these properties are preserved under small perturbations of the iterated function system IFS() with respect to the Lipschitz topology.
{"title":"Iterated Function Systems with the Weak Average Contraction Conditions","authors":"A. Ehsani, F. Ghane","doi":"10.1080/1726037X.2019.1651492","DOIUrl":"https://doi.org/10.1080/1726037X.2019.1651492","url":null,"abstract":"Abstract This paper concerns the chaos game of random iterated function systems. We consider a random iterated function system IFS() generated by a finite family of Lipschitz maps on a compact ball of ℝn with the weak average contraction condition and show that it admits a quasi-attractor satisfying the deterministic chaos game. In particular, these properties are preserved under small perturbations of the iterated function system IFS() with respect to the Lipschitz topology.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"173 - 185"},"PeriodicalIF":0.9,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1651492","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45946424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-03DOI: 10.1080/1726037X.2019.1668148
S. Dey, B. Pal, A. Bhattacharyya
Abstract It is well-known that Einstein manifolds play an important role in geometry as well as in general relativity. Einstein manifolds form a natural subclass of the class of quasi-Einstein manifolds. The object of the present paper is to study some geometric properties of mixed-generalized quasi-Einstein Manifolds (MG(QE)n) which admitting certain vector fields. We show the existence of MG(QE)n, by constructing several non-trivial examples. Finally we study warped product on MG(QE)n and show that M = I×M∗ (dimI = 1 and dimM∗ = n − 1) is a MG(QE)n if M∗ is a generalized quasi-Einstein Manifold (G(QE)n).
{"title":"A Non-Flat Riemannian Manifold Admitting Certain Vectors Fields","authors":"S. Dey, B. Pal, A. Bhattacharyya","doi":"10.1080/1726037X.2019.1668148","DOIUrl":"https://doi.org/10.1080/1726037X.2019.1668148","url":null,"abstract":"Abstract It is well-known that Einstein manifolds play an important role in geometry as well as in general relativity. Einstein manifolds form a natural subclass of the class of quasi-Einstein manifolds. The object of the present paper is to study some geometric properties of mixed-generalized quasi-Einstein Manifolds (MG(QE)n) which admitting certain vector fields. We show the existence of MG(QE)n, by constructing several non-trivial examples. Finally we study warped product on MG(QE)n and show that M = I×M∗ (dimI = 1 and dimM∗ = n − 1) is a MG(QE)n if M∗ is a generalized quasi-Einstein Manifold (G(QE)n).","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"221 - 237"},"PeriodicalIF":0.9,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1668148","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44205460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-03DOI: 10.1080/1726037X.2019.1668146
E. Azizpour, Dordi Mohammad Atayi
Abstract Suppose that = (M, M ) is a graded manifold and consider a direct subsheaf of DerM and a graded vector field Γ on ; both satisfying certain conditions. We associate to the graded vector field Γ ∈ DerM, a set of 1-forms and show that if φ ∈ is a non-degenerate graded 1-form and X ∈ DerM such that for some superfunction f on , then the superfunction F = f − J(φ)(X) satisfies . This result, generalizes the conditions under which there exist a solution for the inverse problem.
{"title":"Dynamical Symmetries for Graded Vector Fields","authors":"E. Azizpour, Dordi Mohammad Atayi","doi":"10.1080/1726037X.2019.1668146","DOIUrl":"https://doi.org/10.1080/1726037X.2019.1668146","url":null,"abstract":"Abstract Suppose that = (M, M ) is a graded manifold and consider a direct subsheaf of DerM and a graded vector field Γ on ; both satisfying certain conditions. We associate to the graded vector field Γ ∈ DerM, a set of 1-forms and show that if φ ∈ is a non-degenerate graded 1-form and X ∈ DerM such that for some superfunction f on , then the superfunction F = f − J(φ)(X) satisfies . This result, generalizes the conditions under which there exist a solution for the inverse problem.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"187 - 203"},"PeriodicalIF":0.9,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1668146","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49433311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-03DOI: 10.1080/1726037X.2019.1668149
G. S. Khadekar, Aina Gupta
Abstract In this paper we consider a correspondence between holographic dark energy density and extended Chaplygin gas energy density proposed by Pourhassan and Kahya [2014] (Advances in High Energy Physics, 231452, 2014) in FRW universe. We solve the Friedmann equation and investigate the be- haviour of cosmological parameters and also we reconstruct the potential and dynamics of the scalar field which describe the extended Chaplygin gas cosmology.
本文考虑了FRW宇宙中全息暗能量密度与Pourhassan和Kahya [2014] (Advances In High energy Physics, 231452, 2014)提出的扩展Chaplygin气体能量密度的对应关系。我们求解了弗里德曼方程，研究了宇宙学参数的be-行为，并重建了描述扩展的查普金气体宇宙学的标量场的势和动力学。
{"title":"Holographic Dark Energy with Extended Chaplygin Gas Model","authors":"G. S. Khadekar, Aina Gupta","doi":"10.1080/1726037X.2019.1668149","DOIUrl":"https://doi.org/10.1080/1726037X.2019.1668149","url":null,"abstract":"Abstract In this paper we consider a correspondence between holographic dark energy density and extended Chaplygin gas energy density proposed by Pourhassan and Kahya [2014] (Advances in High Energy Physics, 231452, 2014) in FRW universe. We solve the Friedmann equation and investigate the be- haviour of cosmological parameters and also we reconstruct the potential and dynamics of the scalar field which describe the extended Chaplygin gas cosmology.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"239 - 266"},"PeriodicalIF":0.9,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1668149","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48872751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-02DOI: 10.1080/1726037X.2018.1453655
A. Hasmani, D. Pandya
ABSTRACT In this paper we have obtained an exact solution for the static spherically symmetric space-time with charged anisotropic fluid distribution in context of Rosen's Bimetric General Relativity (BGR).
{"title":"Spherically Symmetric Static Charged Anisotropic Fluid in Rosen's Bimetric Theory of Gravitation","authors":"A. Hasmani, D. Pandya","doi":"10.1080/1726037X.2018.1453655","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1453655","url":null,"abstract":"ABSTRACT In this paper we have obtained an exact solution for the static spherically symmetric space-time with charged anisotropic fluid distribution in context of Rosen's Bimetric General Relativity (BGR).","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"13 - 21"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1453655","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47271264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-02DOI: 10.1080/1726037X.2018.1551720
A. A. Ansari, Z. Alhussain
ABSTRACT This manuscript investigates the five-body problem with kite configuration where four bodies are placed at the vertices of a kite. All the vertices of kite are taken at the circumference of a circle. These four bodies are considered as primaries which are moving on the circle with same centre which is taken as origin. The fifth infinitesimal body is moving in the space under the influences of these four primaries but not influencing them. After evaluating the equations of motion of the infinitesimal body, we have determined the Jacobi-integral. In the next section, we have done the computational works, where we have plotted the locations of equilibrium points, zero-velocity curves, regions of motion, Poincaré surfaces of section and basins of attraction in different planes (in-plane and out-of-planes). Moreover, we have examined the linear stability of all the equilibrium points and found that all the equilibrium points are unstable.
{"title":"The Restricted Five-Body Problem With Cyclic Kite Configuration","authors":"A. A. Ansari, Z. Alhussain","doi":"10.1080/1726037X.2018.1551720","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1551720","url":null,"abstract":"ABSTRACT This manuscript investigates the five-body problem with kite configuration where four bodies are placed at the vertices of a kite. All the vertices of kite are taken at the circumference of a circle. These four bodies are considered as primaries which are moving on the circle with same centre which is taken as origin. The fifth infinitesimal body is moving in the space under the influences of these four primaries but not influencing them. After evaluating the equations of motion of the infinitesimal body, we have determined the Jacobi-integral. In the next section, we have done the computational works, where we have plotted the locations of equilibrium points, zero-velocity curves, regions of motion, Poincaré surfaces of section and basins of attraction in different planes (in-plane and out-of-planes). Moreover, we have examined the linear stability of all the equilibrium points and found that all the equilibrium points are unstable.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"107 - 91"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1551720","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49292422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-02DOI: 10.1080/1726037X.2018.1551719
Phinao Ramwungzan, K. B. Mangang
ABSTRACT Some dynamical properties of the uniform limit dynamical system have been investigated. It has been found that for a sequences (X, Fn) of dynamical systems having same attractor A and converging uniformly to a dynamical system (X, f), the dynamical system (X, f) has the same attractor A. It has been found that a sequence (X, Fn) of uniformly rigid dynamical systems converging uniformly to a dynamical system (X, f), the dynamical system (X, f) is also uniformly rigid. We have proved that the uniform limit (X, f) of a uniformly convergent sequence of dynamical systems having pseudo orbit tracing property has pseudo orbit tracing property. The expansiveness and the equicontinuous set ϵ: of the uniform limit dynamical system have been investigated.
{"title":"On Attractor and Pseudo Orbit Tracing of Uniform Limit Dynamical Systems","authors":"Phinao Ramwungzan, K. B. Mangang","doi":"10.1080/1726037X.2018.1551719","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1551719","url":null,"abstract":"ABSTRACT Some dynamical properties of the uniform limit dynamical system have been investigated. It has been found that for a sequences (X, Fn) of dynamical systems having same attractor A and converging uniformly to a dynamical system (X, f), the dynamical system (X, f) has the same attractor A. It has been found that a sequence (X, Fn) of uniformly rigid dynamical systems converging uniformly to a dynamical system (X, f), the dynamical system (X, f) is also uniformly rigid. We have proved that the uniform limit (X, f) of a uniformly convergent sequence of dynamical systems having pseudo orbit tracing property has pseudo orbit tracing property. The expansiveness and the equicontinuous set ϵ: of the uniform limit dynamical system have been investigated.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"83 - 90"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1551719","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48070037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-02DOI: 10.1080/1726037X.2018.1551718
B. Tiwari, Ranadip Gangopadhyay, G. K. Prajapati, Manoj Kumar
ABSTRACT In this paper, we have studied spherically symmetric Landsberg metrics with isotropic E-curvature and isotropic S-curvature. In the first case we have shown that the metric reduces to a Berwald metric and therefore, it is of vanishing E-curvature. In the second case we have completely classified the spherically symmetric Landsberg metric with isotropic S-curvature.
{"title":"On Spherically Symmetric Landsberg Metrics","authors":"B. Tiwari, Ranadip Gangopadhyay, G. K. Prajapati, Manoj Kumar","doi":"10.1080/1726037X.2018.1551718","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1551718","url":null,"abstract":"ABSTRACT In this paper, we have studied spherically symmetric Landsberg metrics with isotropic E-curvature and isotropic S-curvature. In the first case we have shown that the metric reduces to a Berwald metric and therefore, it is of vanishing E-curvature. In the second case we have completely classified the spherically symmetric Landsberg metric with isotropic S-curvature.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"71 - 81"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1551718","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43837188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-02DOI: 10.1080/1726037X.2018.1552106
P. Bansal, M. Shahid
ABSTRACT The article is concerned with the etremities for the generalized normalized δ-Casorati curvatures of submanifolds in locally conformal almost cosymplectic manifold endowed with semi-symmetric metric connection using T. Oprea's technique. Applications of these inequalities give rise to several inequalities for hi-slant, hemi-slant, semi-slant, slant, invariant, anti-invariant, CR-submanifolds. Moreover, we characterizes submanifolds on which equalities hold. Also, we establish an inequality in terms of the warping function, the scalar curvature and the Casorati curvature for warped product submanifold of locally conformal almost cosymplectic manifold with semi symmetric metric connection together with some of its applications.
{"title":"Optimization Approach for Extremities of Submanifolds in Locally Conformal Almost Cosymplectic Manifold Admitting SSMC","authors":"P. Bansal, M. Shahid","doi":"10.1080/1726037X.2018.1552106","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1552106","url":null,"abstract":"ABSTRACT The article is concerned with the etremities for the generalized normalized δ-Casorati curvatures of submanifolds in locally conformal almost cosymplectic manifold endowed with semi-symmetric metric connection using T. Oprea's technique. Applications of these inequalities give rise to several inequalities for hi-slant, hemi-slant, semi-slant, slant, invariant, anti-invariant, CR-submanifolds. Moreover, we characterizes submanifolds on which equalities hold. Also, we establish an inequality in terms of the warping function, the scalar curvature and the Casorati curvature for warped product submanifold of locally conformal almost cosymplectic manifold with semi symmetric metric connection together with some of its applications.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"131 - 148"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1552106","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46502438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-02DOI: 10.1080/1726037X.2019.1614248
Hossein Fazli, H. Ebadizadeh
ABSTRACT In this paper, a new rumor spreading model, Ignorant-SpreaderStifler-Controller (ISRC) model, is developed. The model extends the classical Ignorant-Spreader-Stifler (ISR) rumor spreading model by adding a new kind of people that spread a new rumor against previous rumor to control and reduce the maximum rumor influence. We derive a dynamical system that describe the dynamics of the ISRC model. Beside the dynamical analysis of the model, we consider asymptotical stability in equilibrium point. Numerical simulations are also conducted to support our analytic results.
{"title":"Dynamics of Rumor Spreading With a Controller Agent","authors":"Hossein Fazli, H. Ebadizadeh","doi":"10.1080/1726037X.2019.1614248","DOIUrl":"https://doi.org/10.1080/1726037X.2019.1614248","url":null,"abstract":"ABSTRACT In this paper, a new rumor spreading model, Ignorant-SpreaderStifler-Controller (ISRC) model, is developed. The model extends the classical Ignorant-Spreader-Stifler (ISR) rumor spreading model by adding a new kind of people that spread a new rumor against previous rumor to control and reduce the maximum rumor influence. We derive a dynamical system that describe the dynamics of the ISRC model. Beside the dynamical analysis of the model, we consider asymptotical stability in equilibrium point. Numerical simulations are also conducted to support our analytic results.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"61 - 70"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1614248","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60350287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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