Symbolic extensions for partially hyperbolic diffeomorphisms

By Lorenzo J. Díaz, Tom A. Fisher. 2009

50 citations recorded by the source corpus.

We show that every partially hyperbolic diffeomorphism with a 1-dimensional center bundle has a principal symbolic extension. On the other hand, we show there are no symbolic extensions $C^1$-generically among diffeomorphisms containing non-hyperbolic robustly transitive sets with center indecomposable bundle of dimension at least 2.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aa8f6670236e606be8641a6fca215bd004f6b26c

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In Geometry and Topology

1. Jiagang Yang
2. Marcelo Viana
3. Artur Avila
4. A. Zorich
5. Alexander I. Bufetov
6. B. Kalinin
7. V. Sadovskaya

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

Citations in the corpus

• The Entropy Conjecture for Diffeomorphisms away from Tangencies (2010, background): “Weaker versions of the conjecture, where one replaces the spectral radius of f∗ by other topological invariants, have been proved in great generality.”