5,897 research outputs found
Homoclinic intersections of symplectic partially hyperbolic systems with 2D center
We study some generic properties of partially hyperbolic symplectic systems
with 2D center. We prove that generically, every hyperbolic periodic
point has a transverse homoclinic intersection for the maps close to a
direct/skew product of an Anosov diffeomorphism with a map on or
A diffeomorphism with global dominated splitting can not be minimal
Let M be a closed manifold and f be a diffeomorphism on M. We show that if f
has a nontrivial dominated splitting TM=E\oplus F, then f can not be minimal.
The proof mainly use Mane's argument and Liao's selecting lemma.Comment: 5 pages. An application of Liao's selecting lemm
Partially hyperbolic sets with positive measure and for partially hyperbolic systems
In [Discrete Contin. Dyn. Syst. \textbf{15} (2006), no. 3, 811--818.] Xia
introduced a simple dynamical density basis for partially hyperbolic sets of
volume preserving diffeomorphisms. We apply the density basis to the study of
the topological structure of partially hyperbolic sets. We show that if
is a strongly partially hyperbolic set with positive volume, then
contains the global stable manifolds over and
the global unstable manifolds over .
We give several applications of the dynamical density to partially hyperbolic
maps that preserve some . We show that if is essentially accessible
and is an of , then , the map is
transitive, and -a.e. has a dense orbit in . Moreover if
is accessible and center bunched, then either preserves a smooth measure or
there is no of .Comment: Correct the proof of Theorem 5.5. Add a few explanation
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