1996, 2(3): 349-350. doi: 10.3934/dcds.1996.2.349

Stably ergodic skew products

1. 

IBM Research, Watson Research Center, PO Box 218, Yorktown Heights, New York 10598

Received  October 1995 Published  May 1996

In [PS] it is conjectured that among the volume preserving $C^2$ diffeomorphisms of a closed manifold which have some hyperbolicity, the ergodic ones contain an open and dense set. In this paper we prove an analogous statement for skew products of Anosov diffeomorphisms of tori and circle rotations. Thus this paper may be seen as an example of the phenomenon conjectured in [PS]. The corresponding theorem for skew products of Anosov diffeomorphisms and translations of arbitrary compact groups is an interesting open problem.
Citation: Roy Adler, Bruce Kitchens, Michael Shub. Stably ergodic skew products. Discrete & Continuous Dynamical Systems - A, 1996, 2 (3) : 349-350. doi: 10.3934/dcds.1996.2.349
[1]

Viorel Niţică. Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 1197-1204. doi: 10.3934/dcds.2011.29.1197

[2]

Roy Adler, Bruce Kitchens, Michael Shub. Errata to "Stably ergodic skew products" . Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 456-456. doi: 10.3934/dcds.1999.5.456

[3]

Jose S. Cánovas, Antonio Falcó. The set of periods for a class of skew-products. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 893-900. doi: 10.3934/dcds.2000.6.893

[4]

Matúš Dirbák. Minimal skew products with hypertransitive or mixing properties. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1657-1674. doi: 10.3934/dcds.2012.32.1657

[5]

Viorel Nitica. Examples of topologically transitive skew-products. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 351-360. doi: 10.3934/dcds.2000.6.351

[6]

Àlex Haro. On strange attractors in a class of pinched skew products. Discrete & Continuous Dynamical Systems - A, 2012, 32 (2) : 605-617. doi: 10.3934/dcds.2012.32.605

[7]

Eugen Mihailescu, Mariusz Urbański. Transversal families of hyperbolic skew-products. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 907-928. doi: 10.3934/dcds.2008.21.907

[8]

Daniel Guan. Modification and the cohomology groups of compact solvmanifolds. Electronic Research Announcements, 2007, 13: 74-81.

[9]

C.P. Walkden. Stable ergodicity of skew products of one-dimensional hyperbolic flows. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 897-904. doi: 10.3934/dcds.1999.5.897

[10]

Kohei Ueno. Weighted Green functions of nondegenerate polynomial skew products on $\mathbb{C}^2$. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 985-996. doi: 10.3934/dcds.2011.31.985

[11]

Kohei Ueno. Weighted Green functions of polynomial skew products on $\mathbb{C}^2$. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2283-2305. doi: 10.3934/dcds.2014.34.2283

[12]

L. Yu. Glebsky and E. I. Gordon. On approximation of locally compact groups by finite algebraic systems. Electronic Research Announcements, 2004, 10: 21-28.

[13]

Nikolaos Karaliolios. Differentiable Rigidity for quasiperiodic cocycles in compact Lie groups. Journal of Modern Dynamics, 2017, 11: 125-142. doi: 10.3934/jmd.2017006

[14]

Rui Gao, Weixiao Shen. Analytic skew-products of quadratic polynomials over Misiurewicz-Thurston maps. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2013-2036. doi: 10.3934/dcds.2014.34.2013

[15]

David Färm, Tomas Persson. Dimension and measure of baker-like skew-products of $\boldsymbol{\beta}$-transformations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (10) : 3525-3537. doi: 10.3934/dcds.2012.32.3525

[16]

Jory Griffin, Jens Marklof. Limit theorems for skew translations. Journal of Modern Dynamics, 2014, 8 (2) : 177-189. doi: 10.3934/jmd.2014.8.177

[17]

Gunter M. Ziegler. Projected products of polygons. Electronic Research Announcements, 2004, 10: 122-134.

[18]

Adel Alahmadi, Hamed Alsulami, S.K. Jain, Efim Zelmanov. On matrix wreath products of algebras. Electronic Research Announcements, 2017, 24: 78-86. doi: 10.3934/era.2017.24.009

[19]

Andrew M. Zimmer. Compact asymptotically harmonic manifolds. Journal of Modern Dynamics, 2012, 6 (3) : 377-403. doi: 10.3934/jmd.2012.6.377

[20]

Dubi Kelmer. Quantum ergodicity for products of hyperbolic planes. Journal of Modern Dynamics, 2008, 2 (2) : 287-313. doi: 10.3934/jmd.2008.2.287

2016 Impact Factor: 1.099

Metrics

  • PDF downloads (2)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]