Search

For every $r\in \mathbb {N}_{\geq 2}\cup \{\infty \}$, we prove a $C^r$-orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with one-dimensional orientation preserving center bundle. To be precise, for such a diffeomorphism f, if a point y is chain attainable from x through pseudo-orbits, then for any neighborhood U of x and any neighborhood V of y, there exist true orbits from U to V by arbitrarily $C^r$-small perturbations. As a consequence, we prove that for $C^r$-generic diffeomorphisms in this class, periodic points are dense in the chain recurrent set, and chain transitivity implies transitivity.

We construct measures of maximal u-entropy for any partially hyperbolic diffeomorphism that factors over an Anosov torus automorphism and has mostly contracting center direction. The space of such measures has finite dimension, and its extreme points are ergodic measures with pairwise disjoint supports.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

$C^r$-chain closing lemma for certain partially hyperbolic diffeomorphisms

Thermodynamical u-formalism I: measures of maximal u-entropy for maps that factor over Anosov

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

$C^r$-chain closing lemma for certain partially hyperbolic diffeomorphisms

Thermodynamical u-formalism I: measures of maximal u-entropy for maps that factor over Anosov