scholarly journals Historic behavior in nonhyperbolic homoclinic classes

2019 ◽  
Vol 148 (3) ◽  
pp. 1195-1206
Author(s):  
Pablo G. Barrientos ◽  
Shin Kiriki ◽  
Yushi Nakano ◽  
Artem Raibekas ◽  
Teruhiko Soma
Keyword(s):  
Homoclinic Classes

scholarly journals The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms

2020 ◽  
pp. 1-26
Author(s):  
SNIR BEN OVADIA
Keyword(s):  
Symbolic Dynamics ◽  
Full Measure ◽  
Probability Measures ◽  
Positive Entropy ◽  
Surface Diffeomorphisms ◽  
Srb Measures ◽  
Hyperbolic Diffeomorphisms ◽  
Set Of Points ◽  
Math Phys ◽  
Homoclinic Classes

Abstract The papers [O. M. Sarig. Symbolic dynamics for surface diffeomorphisms with positive entropy. J. Amer. Math. Soc.26(2) (2013), 341–426] and [S. Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. J. Mod. Dyn.13 (2018), 43–113] constructed symbolic dynamics for the restriction of $C^r$ diffeomorphisms to a set $M'$ with full measure for all sufficiently hyperbolic ergodic invariant probability measures, but the set $M'$ was not identified there. We improve the construction in a way that enables $M'$ to be identified explicitly. One application is the coding of infinite conservative measures on the homoclinic classes of Rodriguez-Hertz et al. [Uniqueness of SRB measures for transitive diffeomorphisms on surfaces. Comm. Math. Phys.306(1) (2011), 35–49].

scholarly journals Robustly expansive homoclinic classes are generically hyperbolic

2009 ◽  
Vol 24 (4) ◽  
pp. 1325-1333 ◽  
Author(s):  
Martín Sambarino ◽  
◽  
José L. Vieitez ◽  
Keyword(s):  
Homoclinic Classes

scholarly journals Super-exponential growth of the number of periodic orbits inside homoclinic classes

2008 ◽  
Vol 20 (3) ◽  
pp. 589-604 ◽  
Author(s):  
Christian Bonatti ◽  
◽  
Lorenzo J. Díaz ◽  
Todd Fisher ◽  
◽  
...  
Keyword(s):  
Periodic Orbits ◽  
Exponential Growth ◽  
Homoclinic Classes

scholarly journals Homoclinic classes for sectional-hyperbolic sets

2016 ◽  
Vol 56 (3) ◽  
pp. 531-538 ◽  
Author(s):  
Alexander Arbieto ◽  
Andrés Mauricio Lopez Barragán ◽  
Carlos Arnoldo Morales Rojas
Keyword(s):  
Hyperbolic Sets ◽  
Homoclinic Classes

scholarly journals Periodic measures and partially hyperbolic homoclinic classes

2019 ◽  
Vol 372 (2) ◽  
pp. 755-802
Author(s):  
Christian Bonatti ◽  
Jinhua Zhang
Keyword(s):  
Partially Hyperbolic ◽  
Homoclinic Classes

scholarly journals Lyapunov stable homoclinic classes for smooth vector fields

2019 ◽  
Vol 17 (1) ◽  
pp. 990-997
Author(s):  
Manseob Lee
Keyword(s):  
Vector Fields ◽  
Smooth Vector ◽  
Homoclinic Class ◽  
Shadowing Property ◽  
Homoclinic Classes

Abstract In this paper, we show that for generic C1, if a flow Xt has the shadowing property on a bi-Lyapunov stable homoclinic class, then it does not contain any singularity and it is hyperbolic.

Measure expansive homoclinic classes for generic diffeomorphisms

2015 ◽  
Vol 9 ◽  
pp. 3623-3628 ◽  
Author(s):  
Manseob Lee
Keyword(s):  
Homoclinic Classes

scholarly journals Newhouse phenomenon and homoclinic classes

2010 ◽  
Vol 31 (5) ◽  
pp. 1537-1562 ◽  
Author(s):  
JIAGANG YANG
Keyword(s):  
Saddle Point ◽  
Infinite Sequence ◽  
Homoclinic Class ◽  
Generic Subset ◽  
Codimension One ◽  
Homoclinic Tangencies ◽  
Homoclinic Classes

AbstractWe show that for a C1 generic subset of diffeomorphisms far from homoclinic tangencies, any infinite sequence of sinks or sources must accumulate on a homoclinic class of some saddle point with codimension one.

HYPERBOLICITY OF HOMOCLINIC CLASSES OF VECTOR FIELDS

2014 ◽  
Vol 98 (3) ◽  
pp. 375-389 ◽  
Author(s):  
KEONHEE LEE ◽  
MANSEOB LEE ◽  
SEUNGHEE LEE
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Closed Orbit ◽  
Homoclinic Class ◽  
Shadowing Property ◽  
Homoclinic Classes

Let${\it\gamma}$be a hyperbolic closed orbit of a$C^{1}$vector field$X$on a compact$C^{\infty }$manifold$M$and let$H_{X}({\it\gamma})$be the homoclinic class of$X$containing${\it\gamma}$. In this paper, we prove that if a$C^{1}$-persistently expansive homoclinic class$H_{X}({\it\gamma})$has the shadowing property, then$H_{X}({\it\gamma})$is hyperbolic.

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