On the Continuity of the Topological Entropy of Non-autonomous Dynamical Systems

  • Jeovanny de Jesus Muentes Acevedo


Let M be a compact Riemannian manifold. The set \(\text {F}^{r}(M)\) consisting of sequences \((f_{i})_{i\in {\mathbb {Z}}}\) of \(C^{r}\)-diffeomorphisms on M can be endowed with the compact topology or with the strong topology. A notion of topological entropy is given for these sequences. I will prove this entropy is discontinuous at each sequence if we consider the compact topology on \(\text {F}^{r}(M)\). On the other hand, if \( r\ge 1\) and we consider the strong topology on \(\text {F}^{r}(M)\), this entropy is a continuous map.


Topological entropy Strong topology Non-autonomous dynamical systems Non-stationary dynamical systems 

Mathematics Subject Classification

37A35 37B40 37B55 


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Copyright information

© Sociedade Brasileira de Matemática 2017

Authors and Affiliations

  1. 1.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil

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