5 papers · 1 filter
Transitive partially hyperbolic diffeomorphisms in dimension three
Ziqiang Feng
We prove that any transitive conservative partially hyperbolic diffeomorphism of a closed 3-manifold with virtually solvable fundamental group is ergodic. Consequently, i…
Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three
Ziqiang Feng, Raúl Ures
We show that any conservative partially hyperbolic diffeomorphism homotopic to the identity is accessible unless the fundamental group of its ambient 3-manifold is virtually solvab…
Partially Hyperbolic Dynamics with Quasi-isometric Center
Ziqiang Feng
We consider the class of partially hyperbolic diffeomorphisms on a closed 3-manifold with quasi-isometric center. Under the non-wandering condition, we prove that the diffeomorphis…
Accessibility and Ergodicity of Partially Hyperbolic Diffeomorphisms without Periodic Points
Ziqiang Feng, Raúl Ures
We prove that every conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergod…
The Decay Rate of Patterson-Sullivan Measures with Potential Functions and Critical Exponents
Ziqiang Feng, Fei Liu, Fang Wang
Basing upon the recent development of the Patterson-Sullivan measures with a Hölder continuous nonzero potential function, we use tools of both dynamics of geodesic flows and geome…