Pub Date : 2019-01-02DOI: 10.1080/1726037X.2018.1551717
S. Tchuiaga
ABSTRACT This paper continues the study of the group Hameo(M, ω), of all Hamiltonian homeomorphisms of a closed symplectic manifold (M, ω). After given a direct proof of the positivity result of the symplectic displacement energy, we show that the uniqueness theorem of generators of strong symplectic isotopies extends to any closed symplectic manifold: An explicit formula for the mass flow of any strong symplectic isotopy with respect to its generator is given. We show that Hameo(M, ω) inherits under the C0 -Hamiltonian topology, the fragmentation property, the algebraic perfectness, and coincides with the commutator sub-group of the group of all strong symplectic homeomorphisms. This solves a Banyaga's conjecture, and some other conjectures are also formulated.
{"title":"C0–Symplectic Geometry Under Displacements","authors":"S. Tchuiaga","doi":"10.1080/1726037X.2018.1551717","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1551717","url":null,"abstract":"ABSTRACT This paper continues the study of the group Hameo(M, ω), of all Hamiltonian homeomorphisms of a closed symplectic manifold (M, ω). After given a direct proof of the positivity result of the symplectic displacement energy, we show that the uniqueness theorem of generators of strong symplectic isotopies extends to any closed symplectic manifold: An explicit formula for the mass flow of any strong symplectic isotopy with respect to its generator is given. We show that Hameo(M, ω) inherits under the C0 -Hamiltonian topology, the fragmentation property, the algebraic perfectness, and coincides with the commutator sub-group of the group of all strong symplectic homeomorphisms. This solves a Banyaga's conjecture, and some other conjectures are also formulated.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"109 - 129"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1551717","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43531082","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.2018.1564579
M. Lone
ABSTRACT The main objective of the present paper is to generalize the inequalities obtained by the same author M. A. Lone, Filomat, 31:15, pp 4925-4932 and M.A. Lone, Balkan Journal of Geometry and Its Applications, 22(1), pp 41-50 in the contact version. We consider hi-slant submanifolds of Kenmotsu space forms to obtain the inequalities and also discuss the equality case.
本文的主要目的是推广由同一作者M.A. Lone, Filomat, 31:15, pp 4925-4932和M.A. Lone, Balkan Journal of Geometry and Its Applications, 22(1)， pp 41-50在接触版中得到的不等式。我们考虑Kenmotsu空间形式的高倾斜子流形，得到了不等式，并讨论了相等的情况。
{"title":"Optimal Inequalities for Generalized Normalized δ-Casorati Curvatures for Hi-Slant Submanifolds of Kenmotsu Space Forms","authors":"M. Lone","doi":"10.1080/1726037X.2018.1564579","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1564579","url":null,"abstract":"ABSTRACT The main objective of the present paper is to generalize the inequalities obtained by the same author M. A. Lone, Filomat, 31:15, pp 4925-4932 and M.A. Lone, Balkan Journal of Geometry and Its Applications, 22(1), pp 41-50 in the contact version. We consider hi-slant submanifolds of Kenmotsu space forms to obtain the inequalities and also discuss the equality case.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"39 - 50"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1564579","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47791686","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.2018.1564580
S. A. Ahmadi
ABSTRACT In this note we use the concepts of lower density and upper density for elements of Furstenburg families to measure the set of error times in the shadowing process in non-metrizable topological spaces. We show that the measure of errors is the same for all iterations of a dynamical system.
{"title":"A Note on Furstenburg Families and Shadowing in Topological Spaces","authors":"S. A. Ahmadi","doi":"10.1080/1726037X.2018.1564580","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1564580","url":null,"abstract":"ABSTRACT In this note we use the concepts of lower density and upper density for elements of Furstenburg families to measure the set of error times in the shadowing process in non-metrizable topological spaces. We show that the measure of errors is the same for all iterations of a dynamical system.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"51 - 59"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1564580","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41627734","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.2019.1611729
M. Vijaya Santhi, V. Rao, Y. Aditya
ABSTRACT Field equations of f(R) theory of gravity are obtained with the aid of locally rotationally symmetric (LRS) Bianchi type-I metric when the matter source is a bulk viscous fluid containing one dimensional cosmic strings. Applying some physically possible conditions, we have obtained a determinate solution of the field equations. The deceleration parameter of our model exhibits a smooth transition from early decelerated phase to late time accelerating phase. We also find that the realistic energy conditions p ≥ 0 and pp ≤ 0 are satisfied in our model. Some other properties of the model are also discussed.
{"title":"Bianchi Type-I Bulk Viscous String Model in f(R) Gravity","authors":"M. Vijaya Santhi, V. Rao, Y. Aditya","doi":"10.1080/1726037X.2019.1611729","DOIUrl":"https://doi.org/10.1080/1726037X.2019.1611729","url":null,"abstract":"ABSTRACT Field equations of f(R) theory of gravity are obtained with the aid of locally rotationally symmetric (LRS) Bianchi type-I metric when the matter source is a bulk viscous fluid containing one dimensional cosmic strings. Applying some physically possible conditions, we have obtained a determinate solution of the field equations. The deceleration parameter of our model exhibits a smooth transition from early decelerated phase to late time accelerating phase. We also find that the realistic energy conditions p ≥ 0 and pp ≤ 0 are satisfied in our model. Some other properties of the model are also discussed.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"23 - 38"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1611729","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49493110","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.2018.1551291
D. Reddy, Y. Aditya, G. Ramesh
ABSTRACT We have investigated an anisotropic dark energy cosmological model in the presence of anisotropic dark energy fluid coupled with mass less scalar field in KantowskiSachs space-time in general theory of relativity. A physically viable dark energy cosmological model is presented using (i) a hybrid expansion law proposed by Akarsu et al. (JCAP. 01, 022: 2014) and (ii) a relation between the metric potential. The dark energy density, the equation of state (EoS) parameter and the skewness parameters of the model are determined and their physical siguificance is pointed out. The deceleration parameter and the jerk parameter of the model show that there is a smooth transition of the uuiverse from early deceleration to late time acceleration which confirms the observations modem cosmology.
{"title":"Dynamical Anisotropic Dark Energy Cosmological Model in General Relativity","authors":"D. Reddy, Y. Aditya, G. Ramesh","doi":"10.1080/1726037X.2018.1551291","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1551291","url":null,"abstract":"ABSTRACT We have investigated an anisotropic dark energy cosmological model in the presence of anisotropic dark energy fluid coupled with mass less scalar field in KantowskiSachs space-time in general theory of relativity. A physically viable dark energy cosmological model is presented using (i) a hybrid expansion law proposed by Akarsu et al. (JCAP. 01, 022: 2014) and (ii) a relation between the metric potential. The dark energy density, the equation of state (EoS) parameter and the skewness parameters of the model are determined and their physical siguificance is pointed out. The deceleration parameter and the jerk parameter of the model show that there is a smooth transition of the uuiverse from early deceleration to late time acceleration which confirms the observations modem cosmology.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"1 - 12"},"PeriodicalIF":0.9,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1551291","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60349992","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 : 2018-07-03DOI: 10.1080/1726037X.2018.1437941
A. Lesfari
Abstract The aim of this paper is to demonstrate the rich interaction between the properties of dynamical systems, the geometry of its asymptotic solutions, and the theory of Abelian varieties. We are going to illustrate as well that the nature of many methods for finding solutions of some dynamical systems is determined by the Laurent series for solutions of nonlinear differential equations. We apply the methods to the Kowalewski’top a solid body rotating about a fixed point, the Kirchhoff’s equations of motion of a solid in an ideal fluid and the Ramani-Dorizzi-Grammaticos (RDG) series of integrable potentials.
{"title":"Normally generated line bundle and laurent series solutions of nonlinear differential equations","authors":"A. Lesfari","doi":"10.1080/1726037X.2018.1437941","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1437941","url":null,"abstract":"Abstract The aim of this paper is to demonstrate the rich interaction between the properties of dynamical systems, the geometry of its asymptotic solutions, and the theory of Abelian varieties. We are going to illustrate as well that the nature of many methods for finding solutions of some dynamical systems is determined by the Laurent series for solutions of nonlinear differential equations. We apply the methods to the Kowalewski’top a solid body rotating about a fixed point, the Kirchhoff’s equations of motion of a solid in an ideal fluid and the Ramani-Dorizzi-Grammaticos (RDG) series of integrable potentials.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"151 - 171"},"PeriodicalIF":0.9,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1437941","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46566460","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 : 2018-07-03DOI: 10.1080/1726037X.2018.1436271
E. Nešović, U. Öztürk, E. Öztürk
Abstract In this paper, we define T-slant, N-slant and B-slant helices in Galilean space 𝔾3. In particular, we obtain the explicit parameter equations of the T-slant helices and prove that an admissible curve is a T-slant helix with a non-isotropic axis if and only if it has a non-zero constant conical curvature. We also prove that there are no N-slant, B-slant and Darboux helices in the same space.
{"title":"On T-Slant, N-Slant and B-Slant helices in galilean space 𝔾3","authors":"E. Nešović, U. Öztürk, E. Öztürk","doi":"10.1080/1726037X.2018.1436271","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1436271","url":null,"abstract":"Abstract In this paper, we define T-slant, N-slant and B-slant helices in Galilean space 𝔾3. In particular, we obtain the explicit parameter equations of the T-slant helices and prove that an admissible curve is a T-slant helix with a non-isotropic axis if and only if it has a non-zero constant conical curvature. We also prove that there are no N-slant, B-slant and Darboux helices in the same space.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"187 - 199"},"PeriodicalIF":0.9,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1436271","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42458890","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 : 2018-07-03DOI: 10.1080/1726037X.2018.1436273
E. Rezaali, F. Ghane, H. Ebadizadeh
Abstract In this paper, we discuss several stronger forms of sensitivities for iterated function systems (IFSs), such as strong sensitivity and syndetical sensitivity, and obtain some sufficient conditions for an IFS to have such sensitivities. We pay special attention to IFSs acting on the circle S1. We prove that each sensitive IFS acting on the circle S1 generating by a finite family of circle homeomorphisms is strongly sensitive. However, to obtain syndetical sensitivity, we impose some extra conditions on the IFS. Finally, we study sensitivity properties for syndetical transitive IFSs. We show that each syndetically transitive IFS is topologically ergodic.
{"title":"Syndetically transitive and syndetically sensitive Iterated Function Systems","authors":"E. Rezaali, F. Ghane, H. Ebadizadeh","doi":"10.1080/1726037X.2018.1436273","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1436273","url":null,"abstract":"Abstract In this paper, we discuss several stronger forms of sensitivities for iterated function systems (IFSs), such as strong sensitivity and syndetical sensitivity, and obtain some sufficient conditions for an IFS to have such sensitivities. We pay special attention to IFSs acting on the circle S1. We prove that each sensitive IFS acting on the circle S1 generating by a finite family of circle homeomorphisms is strongly sensitive. However, to obtain syndetical sensitivity, we impose some extra conditions on the IFS. Finally, we study sensitivity properties for syndetical transitive IFSs. We show that each syndetically transitive IFS is topologically ergodic.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"129 - 137"},"PeriodicalIF":0.9,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1436273","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44948780","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 : 2018-07-03DOI: 10.1080/1726037X.2018.1436270
Z. Nazari, B. Mosapour
Abstract This paper deals with studying the entropy of dynamical systems on hyperfuzzy sets. At first we define the entropy of hyperfuzzy partitions and conditional entropy. Then, some basic properties of these notions are established. Furthermore, we introduce the notion of a dynamical systems on hyperfuzzy sets and the entropy of it. Finally, we define a generator of this dynamical system and prove Kolmogorov-Sinai’s Theorem is also true for our mentioned generator.
{"title":"The entropy of hyperfuzzy sets","authors":"Z. Nazari, B. Mosapour","doi":"10.1080/1726037X.2018.1436270","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1436270","url":null,"abstract":"Abstract This paper deals with studying the entropy of dynamical systems on hyperfuzzy sets. At first we define the entropy of hyperfuzzy partitions and conditional entropy. Then, some basic properties of these notions are established. Furthermore, we introduce the notion of a dynamical systems on hyperfuzzy sets and the entropy of it. Finally, we define a generator of this dynamical system and prove Kolmogorov-Sinai’s Theorem is also true for our mentioned generator.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"173 - 185"},"PeriodicalIF":0.9,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1436270","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47543459","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 : 2018-07-03DOI: 10.1080/1726037X.2018.1436272
E. Azizpour, M. Zarifi
Abstract Suppose that ℳ = (M, 𝒜M) is a graded manifold and consider a direct subsheaf 𝒟 of Der 𝒜ℳ and a graded vector field Γ on ℳ, both satisfying certain conditions. We attach to 𝒟 a distribution 𝒟 + [Γ, 𝒟] and characterize its maximal rank with respect to dim ℳ. 𝒟 is used to characterize the local expression of Γ.
{"title":"Graded vector fields and involutive distributions on graded manifolds","authors":"E. Azizpour, M. Zarifi","doi":"10.1080/1726037X.2018.1436272","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1436272","url":null,"abstract":"Abstract Suppose that ℳ = (M, 𝒜M) is a graded manifold and consider a direct subsheaf 𝒟 of Der 𝒜ℳ and a graded vector field Γ on ℳ, both satisfying certain conditions. We attach to 𝒟 a distribution 𝒟 + [Γ, 𝒟] and characterize its maximal rank with respect to dim ℳ. 𝒟 is used to characterize the local expression of Γ.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"101 - 127"},"PeriodicalIF":0.9,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1436272","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48340924","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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