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POSITIVELY MEASURE EXPANSIVE AND EXPANDING

Ahn, Jiweon;Lee, Keonhee;Lee, Manseob

  • Received : 2013.07.08
  • Published : 2014.04.30

Abstract

We show that $C^1$-generically, a differentiable map is positively measure expansive if and only if it is expanding.

Keywords

expansive;measure expansive;generic;expanding

References

  1. A. Arbieto, Periodic orbits and expansiveness, Math. Z. 269 (2011), no. 3-4, 801-807. https://doi.org/10.1007/s00209-010-0767-5
  2. R. Mane, Persistent manifolds are normally hyperbolic, Trans. Amer. Math. Soc. 246 (1978), 261-283. https://doi.org/10.1090/S0002-9947-1978-0515539-0
  3. W. L. Reddy, Expanding maps on compact metric spaces, Topology Appl. 13 (1982), no. 3, 327-334. https://doi.org/10.1016/0166-8641(82)90040-2
  4. K. Sakai, Positively expansive differentiable Maps, Acta Math. Sin. (Engl. Ser.) 26 (2010), no. 10, 1839-1846. https://doi.org/10.1007/s10114-010-9149-5
  5. K. Sakai, N. Sumi, and K. Yamamoto, Measure-expansive diffeomorphisms, Preprint.
  6. D. Yang and S. Gan, Expansive homoclinic classes, Nonlinearity 22 (2009), no. 4,729-733. https://doi.org/10.1088/0951-7715/22/4/002

Cited by

  1. Positively measure-expansive differentiable maps vol.435, pp.1, 2016, https://doi.org/10.1016/j.jmaa.2015.10.034

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)