American Institute of Mathematical Sciences

Advanced
October  2008, 20(4): 1029-1038. doi: 10.3934/dcds.2008.20.1029

Semi-hyperbolicity and hyperbolicity

Marcin Mazur 1, , Jacek Tabor 1, and  Piotr Kościelniak 1,

1. 

Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków, Poland, Poland, Poland

Received  February 2007 Revised  September 2007 Published  January 2008

We prove that for $\mathcal{C}^1$-diffeomorfisms semi-hyperbolicity of an invariant set implies its hyperbolicity. Moreover, we provide some exact estimations of hyperbolicity constants by semi-hyperbolicity ones, which can be useful in strict numerical computations.
Keywords: numerical computations., Hyperbolicity, semi-hyperbolicity.
Mathematics Subject Classification: Primary: 37D05, 37D20, Secondary: 37M9.
Citation: Marcin Mazur, Jacek Tabor, Piotr Kościelniak. Semi-hyperbolicity and hyperbolicity. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1029-1038. doi: 10.3934/dcds.2008.20.1029
[1]

Marcin Mazur, Jacek Tabor. Computational hyperbolicity. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1175-1189. doi: 10.3934/dcds.2011.29.1175
[2]

Boris Hasselblatt, Yakov Pesin, Jörg Schmeling. Pointwise hyperbolicity implies uniform hyperbolicity. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2819-2827. doi: 10.3934/dcds.2014.34.2819
[3]

Luis Barreira, Claudia Valls. Growth rates and nonuniform hyperbolicity. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 509-528. doi: 10.3934/dcds.2008.22.509
[4]

Rasul Shafikov, Christian Wolf. Stable sets, hyperbolicity and dimension. Discrete and Continuous Dynamical Systems, 2005, 12 (3) : 403-412. doi: 10.3934/dcds.2005.12.403
[5]

Sergey Kryzhevich, Sergey Tikhomirov. Partial hyperbolicity and central shadowing. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2901-2909. doi: 10.3934/dcds.2013.33.2901
[6]

Arno Berger. On finite-time hyperbolicity. Communications on Pure and Applied Analysis, 2011, 10 (3) : 963-981. doi: 10.3934/cpaa.2011.10.963
[7]

Christian Bonatti, Shaobo Gan, Dawei Yang. On the hyperbolicity of homoclinic classes. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1143-1162. doi: 10.3934/dcds.2009.25.1143
[8]

Mickaël Kourganoff. Uniform hyperbolicity in nonflat billiards. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1145-1160. doi: 10.3934/dcds.2018048
[9]

Andy Hammerlindl, Jana Rodriguez Hertz, Raúl Ures. Ergodicity and partial hyperbolicity on Seifert manifolds. Journal of Modern Dynamics, 2020, 0: 331-348. doi: 10.3934/jmd.2020012
[10]

Zhenning Cai, Yuwei Fan, Ruo Li. On hyperbolicity of 13-moment system. Kinetic and Related Models, 2014, 7 (3) : 415-432. doi: 10.3934/krm.2014.7.415
[11]

Federico Rodriguez Hertz, María Alejandra Rodriguez Hertz, Raúl Ures. Partial hyperbolicity and ergodicity in dimension three. Journal of Modern Dynamics, 2008, 2 (2) : 187-208. doi: 10.3934/jmd.2008.2.187
[12]

Jana Rodriguez Hertz. Genericity of nonuniform hyperbolicity in dimension 3. Journal of Modern Dynamics, 2012, 6 (1) : 121-138. doi: 10.3934/jmd.2012.6.121
[13]

Jérôme Buzzi, Todd Fisher. Entropic stability beyond partial hyperbolicity. Journal of Modern Dynamics, 2013, 7 (4) : 527-552. doi: 10.3934/jmd.2013.7.527
[14]

Yi Shi, Shaobo Gan, Lan Wen. On the singular-hyperbolicity of star flows. Journal of Modern Dynamics, 2014, 8 (2) : 191-219. doi: 10.3934/jmd.2014.8.191
[15]

Yakov Pesin. On the work of Dolgopyat on partial and nonuniform hyperbolicity. Journal of Modern Dynamics, 2010, 4 (2) : 227-241. doi: 10.3934/jmd.2010.4.227
[16]

Luis Barreira, Claudia Valls. Regularity of center manifolds under nonuniform hyperbolicity. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 55-76. doi: 10.3934/dcds.2011.30.55
[17]

Dawei Yang, Shaobo Gan, Lan Wen. Minimal non-hyperbolicity and index-completeness. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1349-1366. doi: 10.3934/dcds.2009.25.1349
[18]

Shmuel Friedland, Gunter Ochs. Hausdorff dimension, strong hyperbolicity and complex dynamics. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 405-430. doi: 10.3934/dcds.1998.4.405
[19]

Andy Hammerlindl. Partial hyperbolicity on 3-dimensional nilmanifolds. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3641-3669. doi: 10.3934/dcds.2013.33.3641
[20]

David Damanik, Jake Fillman, Milivoje Lukic, William Yessen. Characterizations of uniform hyperbolicity and spectra of CMV matrices. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 1009-1023. doi: 10.3934/dcdss.2016039

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (64)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy