Pub Date : 2023-10-20DOI: 10.1007/s10884-023-10317-8
C. A. Morales, T. Nguyen
{"title":"Quantifying the Shadowing Property","authors":"C. A. Morales, T. Nguyen","doi":"10.1007/s10884-023-10317-8","DOIUrl":"https://doi.org/10.1007/s10884-023-10317-8","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"178 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-20DOI: 10.1007/s10884-023-10321-y
Lianzhang Bao, Wenxian Shen
{"title":"Vanishing-Spreading Dichotomy in a Two-Species Chemotaxis Competition System with a Free Boundary","authors":"Lianzhang Bao, Wenxian Shen","doi":"10.1007/s10884-023-10321-y","DOIUrl":"https://doi.org/10.1007/s10884-023-10321-y","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"28 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135513779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-20DOI: 10.1007/s10884-023-10320-z
Thieu Huy Nguyen, Thi Ngoc Ha Vu
{"title":"Dichotomy Gap Conditions, Admissible Spaces, and Inertial Manifolds","authors":"Thieu Huy Nguyen, Thi Ngoc Ha Vu","doi":"10.1007/s10884-023-10320-z","DOIUrl":"https://doi.org/10.1007/s10884-023-10320-z","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-11DOI: 10.1007/s10884-023-10312-z
Jorge A. León, David Márquez-Carreras, Josep Vives
Abstract In the present paper, we study different types of stability of the solution of a semi-linear anticipating stochastic differential equation driven by a Brownian motion, with a random variable as initial condition. The involved stochastic integral is the Skorohod one. Being the initial condition random, we need to redefine the stability concepts. The new stability criteria depend on the derivative of the initial condition in the Malliavin calculus sense.
{"title":"Stability of Some Anticipating Semilinear Stochastic Differential Equations of Skorohod Type","authors":"Jorge A. León, David Márquez-Carreras, Josep Vives","doi":"10.1007/s10884-023-10312-z","DOIUrl":"https://doi.org/10.1007/s10884-023-10312-z","url":null,"abstract":"Abstract In the present paper, we study different types of stability of the solution of a semi-linear anticipating stochastic differential equation driven by a Brownian motion, with a random variable as initial condition. The involved stochastic integral is the Skorohod one. Being the initial condition random, we need to redefine the stability concepts. The new stability criteria depend on the derivative of the initial condition in the Malliavin calculus sense.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136209498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s10884-023-10314-x
Archishman Saha, Cristina Stoica
{"title":"Block Regularisation of the Logarithm Central Force Problem","authors":"Archishman Saha, Cristina Stoica","doi":"10.1007/s10884-023-10314-x","DOIUrl":"https://doi.org/10.1007/s10884-023-10314-x","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-05DOI: 10.1007/s10884-023-10313-y
Divya Khurana
{"title":"Smooth Anosov Katok Diffeomorphisms with Generic Measure","authors":"Divya Khurana","doi":"10.1007/s10884-023-10313-y","DOIUrl":"https://doi.org/10.1007/s10884-023-10313-y","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135482063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-05DOI: 10.1007/s10884-023-10311-0
Adam Czornik, Konrad Kitzing, Stefan Siegmund
{"title":"Spectra Based on Bohl Exponents and Bohl Dichotomy for Nonautonomous Difference Equations","authors":"Adam Czornik, Konrad Kitzing, Stefan Siegmund","doi":"10.1007/s10884-023-10311-0","DOIUrl":"https://doi.org/10.1007/s10884-023-10311-0","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"167 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135482066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-23DOI: 10.1007/s10884-023-10310-1
Ka Man Yim, Vidit Nanda
Abstract The Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of any compact, connected isolated critical set of such a function with high confidence from a sufficiently large finite point sample. The main construction of this paper is a specific index pair which is local to the critical set in question. We establish that these index pairs have positive reach and hence admit a sampling theory for robust homology inference. This allows us to estimate the Conley index, and as a direct consequence, we are also able to estimate the Morse index of any critical point of a Morse function using finitely many local evaluations.
{"title":"Topological Inference of the Conley Index","authors":"Ka Man Yim, Vidit Nanda","doi":"10.1007/s10884-023-10310-1","DOIUrl":"https://doi.org/10.1007/s10884-023-10310-1","url":null,"abstract":"Abstract The Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of any compact, connected isolated critical set of such a function with high confidence from a sufficiently large finite point sample. The main construction of this paper is a specific index pair which is local to the critical set in question. We establish that these index pairs have positive reach and hence admit a sampling theory for robust homology inference. This allows us to estimate the Conley index, and as a direct consequence, we are also able to estimate the Morse index of any critical point of a Morse function using finitely many local evaluations.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135958954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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