A recurrent set for one-dimensional dynamical systems

In this note we introduce a new kind of recurrent set for a dynamical system on the interval [0,1]. This set is not necessarily invariant under continuous conjugacies, but it is invariant under absolutely continuous ones.

___

  • S. A. Ahmadi. On the topology of the chain recurrent set of a dynamical system. Applied general topology, 15(2):167–174, 2014.
  • J. M. Alongi and G. S. Nelson. Recurrence and topology, volume 85. American Mathematical Soc., 2007.
  • N. Aoki and K. Hiraide. Topological theory of dynamical systems: recent advances, volume 52. Elsevier, 1994.
  • P. Krupski, K. Omiljanowski, and K. Ungeheuer. Chain recurrent sets of generic mappings on compact spaces. Topology and its Applications, 202:251 – 268, 2016.
  • S. Li. Dynamical properties of the shift maps on the inverse limit spaces. Ergodic Theory and Dynamical Systems, 12(01):95–108, 1992.
  • N. Shekutkovski and M. Shoptrajanov. Intrinsic shape of the chain recurrent set. Topology and its Applications, 202:117 – 126, 2016.
  • T. Shimomura. Special homeomorphisms and approximation for cantor systems. Topology and its Applications, 161:178 – 195, 2014.
  • S. Spataru. An absolutely continuous function whose inverse functionis not absolutely continuous. Note di Matematica, 23(1):47–49, 2004.
  • X. Wen and L. Wen. Codimension one structurally stable chain classes. Transactions of the American Mathematical Society, 368(6):3849–3870, 2016.