Stable ergodicity of skew products of one-dimensional hyperbolic flows

Discrete and Continuous Dynamical Systems

Volumn 5, Issue 4, 1999, Pages 897-904

  Walkden, C P ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Hyperbolic flow; Skew product; Stable ergodicity; Symbolic flow

Indexed keywords

EID: 0033410098     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.1999.5.897     Document Type: Article

References (13)

1. R. L. Adler, B. Kitchens, and M. Shub, Stably ergodic skew products, Discrete and continuous dynamical systems 2 (1996), 349-350.
2. R. Bowen, One-dimensional hyperbolic sets for flows, J. Diff. Eq. 12 (1972), 173-179.
3. R. Bowen and P. Walters, Expansive one-parameter flows, J. Diff. Eq. 12 (1972), 180-193.
4. M. Field and W. Parry, Stable ergodicity of skew extensions by compact Lie groups, Topology 38 (1999), 167-187.
5. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, C.U.P., 1995.
6. H. B. Keynes and D. Newton, The structure of ergodic measures for compact group extensions, Isr. J. Math. 18 (1974), 363-389.
7. W. Parry, Skew products of shifts with a compact Lie group, J. London Math. Soc. 56 (1997), 395-404.
8. W. Parry and M. Pollicott, Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics, Astérique, vol. 187-188, Société Mathématique de France, 1990.
9. W. Parry and M. Pollicott, Stability of mixing for toral extensions of hyperbolic systems, Proc. Steklov. Inst. 216 (1997), 350-359.
10. D. Rudolph, Classifying the isometric extensions of a Bernoulli shift, J. D'Anal. Math. 34 (1978), 36-60.
11. D. Ruelle, Resonances for Axiom A flows, J. Diff. Geom. 25 (1987), 99-116.
12. C. P. Walkden, Livs̄ic theorems for hyperbolic flows, Trans. Amer. Math. Soc., to appear.
13. C. P. Walkden, Stable ergodic properties of cocycles over hyperbolic attractors, Commun. Math. Phys., to appear.