ACCESSIBILITY OF PARTIALLY HYPERBOLIC ENDOMORPHISMS WITH 1D CENTER-BUNDLES

Baolin He

doi:10.11948/2017022

2017 Volume 7 Issue 1

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Baolin He. ACCESSIBILITY OF PARTIALLY HYPERBOLIC ENDOMORPHISMS WITH 1D CENTER-BUNDLES[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 334-345. doi: 10.11948/2017022

Citation:

Baolin He. ACCESSIBILITY OF PARTIALLY HYPERBOLIC ENDOMORPHISMS WITH 1D CENTER-BUNDLES[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 334-345. doi: 10.11948/2017022

ACCESSIBILITY OF PARTIALLY HYPERBOLIC ENDOMORPHISMS WITH 1D CENTER-BUNDLES

Baolin He

Mathematics and Science College, Shanghai Normal University, Guilin Road, 200234 Shanghai, China

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Abstract

Abstract

We prove that partially hyperbolic endomorphisms with one dimensional center-bundles and non-trivial unstable bundles are stably accessible. And there is residual subset R of partially hyperbolic volume preserving endomorphisms with one dimensional center-bundles such that every f ∈ R is stably accessible. In the end, we prove the accessibility of Gan's example.
- Accessibility /
- partially hyperbolic endomorphisms /
- unstable manifolds /
- orbit space /
- universal covering space
MSC: 37D30;37A25

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References

[1]	D. V. Anosov, Ergodic properties of geodesic flows on closed Riemannian manifolds of negative curvature, (Russian) Dokl. Akad. Nauk SSSR, 151(1963), 1250-1252. Google Scholar
[2]	C. Bonatti, L. J. Daz and M. Viana, Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective, Encyclopaedia of Mathematical Sciences, 102. Mathematical Physics, Ⅲ. Springer-Verlag, Berlin, 2005. xviii+384 pp. Google Scholar
[3]	M. I. Brin and Ja. B. Pesin, Partially hyperbolic dynamical systems, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 38(1974), 170-212. Google Scholar
[4]	K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems, Ann. of Math., 171(2010)(1), 451-489. Google Scholar
[5]	P. Didier, Stability of accessibility, Ergodic theory Dyn.Syst., 23(2003), 1717-1731. Google Scholar
[6]	M. Grayson, C. Pugh and M. Shub, Stably ergodic diffeomorphisms, Ann. of Math., 140(1994)(2), 295-329. Google Scholar
[7]	B. L. He, Accessibility of partially hyperbolic endomorphisms with 1D centerbundles, In preparing. Google Scholar
[8]	F. R. Hertz, M. R. Hertz and R. Ures, Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundles, Invent.math., 172(2008), 353-381. Google Scholar
[9]	M. W. Hirsch, C. C. Pugh and M. Shub, Invariant manifolds. Lecture Notes in Mathematics, Vol. 583. Springer-Verlag, Berlin-New York, 1977. ii+149 pp. Google Scholar
[10]	F. Przytycki, Anosov endomorphisms, Studia Math., 58(1976), 249-285. Google Scholar
[11]	C. Pugh and M. Shub, Stable ergodicity and partial hyperbolicity, International Conference on Dynamical Systems (Montevideo, 1995), 182-187, Pitman Res. Notes Math. Ser., 362, Longman, Harlow, 1996. Google Scholar
[12]	C. Pugh and M. Shub, Ergodicity of Anosov actions, Invent. Math., 15(1972), 1-23. Google Scholar
[13]	M. Qian and Z. S. Zhang, Ergodic theory for Axiom A endomorphisms, Ergodic Theory Dynam. Systems, 15(1995)(1), 161-174. Google Scholar
[14]	M. Qian and S. Zhu, SRB measures and Pesin's entropy formula for endomorphisms, Trans. Amer. Math. Soc., 354(2002)(4), 1453-1471. Google Scholar