RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 6, Pages 19–44 (Mi izv678)

The regularity of central leaves of partially hyperbolic sets and its applications

A. S. Gorodetski

California Institute of Technology

Abstract: We consider partially hyperbolic maps which are close to the direct product of a hyperbolic map and an identity map and prove that their central leaves depend Hölder continuously on the base point in the $C^r$-metric. We use this result to construct an open set of diffeomorphisms with rather unusual properties (they have transitive sets with periodic points of different indices and orbits with zero Lyapunov exponent). This paper concludes a series of joint papers with Yu. S. Ilyashenko.

DOI: https://doi.org/10.4213/im678

Full text: PDF file (702 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2006, 70:6, 1093–1116

Bibliographic databases:

UDC: 517.938
MSC: 37D30, 37C20

Citation: A. S. Gorodetski, “The regularity of central leaves of partially hyperbolic sets and its applications”, Izv. RAN. Ser. Mat., 70:6 (2006), 19–44; Izv. Math., 70:6 (2006), 1093–1116

Citation in format AMSBIB
\Bibitem{Gor06} \by A.~S.~Gorodetski \paper The regularity of central leaves of partially hyperbolic sets and its applications \jour Izv. RAN. Ser. Mat. \yr 2006 \vol 70 \issue 6 \pages 19--44 \mathnet{http://mi.mathnet.ru/izv678} \crossref{https://doi.org/10.4213/im678} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2285025} \zmath{https://zbmath.org/?q=an:1136.37019} \elib{http://elibrary.ru/item.asp?id=9433305} \transl \jour Izv. Math. \yr 2006 \vol 70 \issue 6 \pages 1093--1116 \crossref{https://doi.org/10.1070/IM2006v070n06ABEH002340} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000244954500002} \elib{http://elibrary.ru/item.asp?id=14740957} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33947645943} 

• http://mi.mathnet.ru/eng/izv678
• https://doi.org/10.4213/im678
• http://mi.mathnet.ru/eng/izv/v70/i6/p19

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. A. Kleptsyn, M. B. Nalsky, “Stability of Existence of Nonhyperbolic Measures for $C^1$-Diffeomorphisms”, Funct. Anal. Appl., 41:4 (2007), 271–283
2. Ilyashenko Yu. S., Kleptsyn V. A., Saltykov P., “Openness of the set of boundary preserving maps of an annulus with intermingled attracting basins”, J. Fixed Point Theory Appl., 3:2 (2008), 449–463
3. Diaz L. J., Gorodetski A., “Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes”, Ergodic Theory Dynam. Systems, 29:5 (2009), 1479–1513
4. A. V. Osipov, “Nondensity of the orbital shadowing property in $C^1$-topology”, St. Petersburg Math. J., 22:2 (2011), 267–292
5. Ilyashenko Yu., Negut A., “Invisible parts of attractors”, Nonlinearity, 23:5 (2010), 1199–1219
6. Ilyashenko Yu., “Thick attractors of boundary preserving diffeomorphisms”, Indag. Math. (N.S.), 22:3-4 (2011), 257–314
7. V. A. Kleptsyn, P. S. Saltykov, “On $C^2$-stable effects of intermingled basins of attractors in classes of boundary-preserving maps”, Trans. Moscow Math. Soc., 72 (2011), 193–217
8. Yu Ilyashenko, A Negut, “Hölder properties of perturbed skew products and Fubini regained”, Nonlinearity, 25:8 (2012), 2377
9. N. A. Solodovnikov, “Boundary-preserving mappings of a manifold with intermingling basins of components of the attractor, one of which is open”, Trans. Moscow Math. Soc., 75 (2014), 69–76
10. Barrientos P.G., Ki Yu., Raibekas A., “Symbolic Blender- Horseshoes and Applications”, Nonlinearity, 27:12 (2014), 2805–2839
11. Volk D., “Persistent Massive Attractors of Smooth Maps”, Ergod. Theory Dyn. Syst., 34:2 (2014), 693–704
12. Ali Tahzibi, Andrey Gogolev, “Center Lyapunov exponents in partially hyperbolic dynamics”, JMD, 8:3/4 (2015), 549
13. J. Math. Sci. (N. Y.), 209:6 (2015), 979–987
14. Ilyashenko Yu., Romaskevich O., “Sternberg Linearization Theorem for Skew Products”, J. Dyn. Control Syst., 22:3 (2016), 595–614
15. Gorodetski A., Pesin Ya., “Path Connectedness and Entropy Density of the Space of Hyperbolic Ergodic Measures”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, eds. Katok A., Pesin Y., Hertz F., Amer Mathematical Soc, 2017, 111–121
16. Ilyashenko Yu., Shilin I., “Attractors and Skew Products”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, eds. Katok A., Pesin Y., Hertz F., Amer Mathematical Soc, 2017, 155–175
•  Number of views: This page: 289 Full text: 78 References: 54 First page: 4