Journals
- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
-
Electronic Research Announcements
-
Conference Publications
-
AIMS Mathematics
DCDS
We study a problem raised by Abdenur et. al. [3] that asks,
for any chain transitive set $\Lambda$ of a generic diffeomorphism
$f$, whether the set $I(\Lambda)$ of indices of hyperbolic periodic
orbits that approach $\Lambda$ in the Hausdorff metric must be an
"interval", i.e., whether $\alpha\in I(\Lambda)$ and $\beta\in
I(\Lambda)$, $\alpha<\beta$, must imply $\gamma\in I(\Lambda)$ for
every $\alpha<\gamma<\beta$. We prove this is indeed the case if, in
addition, $f$ is $C^1$ away from homoclinic tangencies and if
$\Lambda$ is a minimally non-hyperbolic set.
DCDS
We give a sufficient criterion for the hyperbolicity of a homoclinic
class. More precisely, if the homoclinic class $H(p)$ admits a
partially hyperbolic splitting $T_{H(p)}M=E^s\oplus_{_<}F$, where
$E^s$ is uniformly contracting and $\dim E^s= \ $ind$(p)$, and all
periodic points homoclinically related with $p$ are uniformly
$E^u$-expanding at the period, then $H(p)$ is hyperbolic. We also
give some consequences of this result.
Year of publication
Related Authors
Related Keywords
[Back to Top]