DOI QR코드

DOI QR Code

BOWEN'S DECOMPOSITION THEOREM FOR TOPOLOGICALLY ANOSOV HOMEOMORPHISMS ON NONCOMPACT AND NON-METRIZABLE SPACES

  • Das, Ruchi (Department of Mathematics Faculty of Mathematical Sciences University of Delhi) ;
  • Das, Tarun (Department of Mathematics Faculty of Mathematical Sciences University of Delhi) ;
  • Shah, Sejal (Department of Mathematics Faculty of Science The Maharaja Sayajirao University of Baroda)
  • 투고 : 2017.03.09
  • 심사 : 2017.05.30
  • 발행 : 2018.01.31

초록

We extend Bowen's decomposition theorem to topologically Anosov homeomorphisms on first countable, locally compact, paracompact, Hausdorff spaces which are not necessarily metrizable and not necessarily compact.

키워드

참고문헌

  1. F. Abdenur and S. Crovisier, Transitivity and topological mixing for $C^1$ diffeomorphisms, Essays in Mathematics and its Applications, 1-16, Springer, Heidelberg, 2012.
  2. E. Akin and J. Auslander, Compacti cations of dynamical systems, arXiv:1004.0323 (2010).
  3. N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, North-Holland Pub-lishing Co., Amsterdam, 1994.
  4. M. Awartani and S. Elaydi, An extension of chaotic dynamics to general topological spaces, Panamer. Math. J. 10 (2000), no. 2, 61-71.
  5. A. M. Blokh, The spectral decomposition for one-dimensional maps, Dynamics reported, 1-59, Dynam. Report. Expositions Dynam. Systems (N.S.), 4, Springer, Berlin, 1995.
  6. R. Bowen, Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc. 154 (1971), 377-397.
  7. R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math. 470, Springer-Verlag, 1975.
  8. T. Ceccherini-Silberstein and M. Coornaert, Sensitivity and Devaney's chaos in uniform spaces, J. Dyn. Control Syst. 19 (2013), no. 3, 349-357. https://doi.org/10.1007/s10883-013-9182-7
  9. C. Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series in Mathematics 38. American Mathematical Society, Providence, R.I., 1978.
  10. T. Das, K. Lee, D. Richeson, and J. Wiseman, Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces, Topology Appl. 160 (2013), no. 1, 149-158. https://doi.org/10.1016/j.topol.2012.10.010
  11. J. Kelley, General Topology, D. Van Nostrand Company Inc., Toronto, New York, Lon-don, 1955.
  12. C. Morales and V. Sirvent, Expansivity for measures on uniform spaces, Trans. Amer. Math. Soc. 368 (2016), no. 8, 5399-5414.
  13. S. Shah, R. Das, and T. Das, Specification property for topological spaces, J. Dyn. Control Syst. 22 (2016), no. 4, 615-622. https://doi.org/10.1007/s10883-015-9275-6
  14. S. Shah, R. Das, and T. Das, A note on uniform entropy for maps having topological speci cation property, Appl. Gen. Topol. 17 (2016), no. 2, 123-127. https://doi.org/10.4995/agt.2016.4555
  15. K. Sigmund, On mixing measures for axiom A diffeomorphisms, Proc. Amer. Math. Soc. 36 (1972), 497-504.
  16. S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. https://doi.org/10.1090/S0002-9904-1967-11798-1
  17. A. Weil, Sur les espaces a structure uniforme et sur la topologie generale, Actual. Sci. Ind., Hermann et Cie., Paris 551, 1937.
  18. R.-S. Yang, Topological Anosov maps of non-compact metric spaces, Northeast. Math. J. 17 (2001), 120-126.