A survey on partially hyperbolic dynamics

By F. R. Hertz, M. R. Hertz, R. Ures. 2006

78 citations recorded by the source corpus.

Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7) Transitivity and (8) Classification. Here we will survey the state of the art on these subjects, and propose related problems.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ab9c59a908b3e695ce3c4c226d7e8f0f30f628db

How researchers see this paper

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In Mathematical Physics

1. F. R. Hertz
2. R. Ures
3. A. Tahzibi
4. J. R. Hertz
5. Artur Avila
6. Marcelo Viana
7. Jiagang Yang

In Statistical and Nonlinear Physics

1. F. R. Hertz
2. R. Ures
3. A. Tahzibi
4. J. R. Hertz
5. Marcelo Viana
6. Jiagang Yang
7. Artur Avila

Citations in the corpus

• Accessibility (2018, unknown): “Partial resolutions exist for C 1 normally hyperbolic foliations [HPS77], C 0 normally hyperbolic foliations with bi-Lyapunov stable actions [HHU07a], and quasi-isometric actions [Ber13].”
• New criteria for ergodicity and nonuniform hyperbolicity (2009, background): “In the last years, many advances have been made in the direction of this conjecture, a survey of which can be found in [33].”