Entropy-expansiveness for partially hyperbolic diffeomorphisms

By Tom A. Fisher, Lorenzo J. Díaz, Maria José Pacifico, J. Vieitez. 2010

72 citations recorded by the source corpus.

We show that diffeomorphisms with a dominated splitting of the form $E^s\oplus E^c\oplus E^u$, where $E^c$ is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular, they have a principal symbolic extension and equilibrium states.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8bb8e208abe9b3e3e70c0a7f10640f8828494e85

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Jiagang Yang
2. Marcelo Viana
3. Li Gang
4. Artur Avila
5. F. R. Hertz
6. José F. Alves
7. C. Bonatti
8. Dmitry Dolgopyat

In Statistical and Nonlinear Physics

1. Jiagang Yang
2. Marcelo Viana
3. Li Gang
4. Artur Avila
5. F. R. Hertz
6. C. Bonatti
7. Dmitry Dolgopyat
8. A. Zorich

Citations in the corpus

• The Entropy Conjecture for Diffeomorphisms away from Tangencies (2010, background): “Let us also point out that Dı́az, Fisher, Pacifico and Vieitez [11, 26] have recently constructed principal symbolic extensions for partially hyperbolic diffeomorphisms admitting an invariant splitting into one-dimensional subbundles.”