Pointwise Dynamics Under Orbital Convergence

  • Abdul Gaffar Khan
  • Pramod Kumar Das
  • Tarun DasEmail author


We obtain sufficient conditions under which the limit of a sequence of functions exhibits a particular dynamical behaviour at a point like expansivity, shadowing, mixing, sensitivity and transitivity. We provide examples to show that the set of all expansive, positively expansive and sensitive points are neither open nor closed in general. We also observe that the set of all transitive and mixing points are closed but not open in general. We give examples to show that properties like expansivity, sensitivity, shadowing, transitivity and mixing at a point need not be preserved under uniform convergence and properties like topological stability and \(\alpha \)-persistence at a point need not be preserved under pointwise convergence.


Expansivity Shadowing Transitivity Topological Stability Chaos 

Mathematics Subject Classification

Primary 54H20 Secondary 40A30 



The first author is supported by CSIR-Junior Research Fellowship (File No.-09/045(1558)/ 2018-EMR-I) of Government of India. The authors express sincere thanks to the reviewer for suggestions.


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Copyright information

© Sociedade Brasileira de Matemática 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesUniversity of DelhiDelhiIndia
  2. 2.School of Mathematical SciencesNarsee Monjee Institute of Management StudiesMumbaiIndia

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