scholarly journals Orbital Shadowing for -Generic Volume-Preserving Diffeomorphisms

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Manseob Lee
Keyword(s):  
Shadowing Property ◽  
Orbital Shadowing ◽  
Volume Preserving

We show that -generically, if a volume-preserving diffeomorphism has the orbital shadowing property, then the diffeomorphism is Anosov.

scholarly journals Asymptotic orbital shadowing property for diffeomorphisms

2019 ◽  
Vol 17 (1) ◽  
pp. 191-201 ◽  
Author(s):  
Manseob Lee
Keyword(s):  
Riemannian Manifold ◽  
Anosov Diffeomorphism ◽  
Shadowing Property ◽  
Orbital Shadowing ◽  
Volume Preserving

Abstract Let M be a closed smooth Riemannian manifold and let f : M → M be a diffeomorphism. We show that if f has the C1 robustly asymptotic orbital shadowing property then it is an Anosov diffeomorphism. Moreover, for a C1 generic diffeomorphism f, if f has the asymptotic orbital shadowing property then it is a transitive Anosov diffeomorphism. In particular, we apply our results to volume-preserving diffeomorphisms.

scholarly journals Orbital shadowing property on chain transitive sets for generic diffeomorphisms

2020 ◽  
Vol 12 (1) ◽  
pp. 146-154
Author(s):  
Manseob Lee
Keyword(s):  
Maximal Chain ◽  
Dimensional Manifold ◽  
Dominated Splitting ◽  
Shadowing Property ◽  
Orbital Shadowing ◽  
Locally Maximal ◽  
Chain Transitive Sets

AbstractLet f : M → M be a diffeomorphism on a closed smooth n(≥ 2) dimensional manifold M. We show that C1 generically, if a diffeomorphism f has the orbital shadowing property on locally maximal chain transitive sets which admits a dominated splitting then it is hyperbolic.

Volume-Preserving Diffeomorphisms with Various Limit Shadowing

2015 ◽  
Vol 25 (02) ◽  
pp. 1550018 ◽  
Author(s):  
Manseob Lee
Keyword(s):  
Shadowing Property ◽  
Limit Shadowing ◽  
Volume Preserving

We present the following: (1) if a volume-preserving diffeomorphism has C1-robustly various limit shadowing property, then it is Anosov; (2) C1-generically, if a volume-preserving diffeomorphism has various limit shadowing property, then it is Anosov.

scholarly journals ORBITAL SHADOWING PROPERTY

2008 ◽  
Vol 45 (4) ◽  
pp. 645-650 ◽  
Author(s):  
Bahman Honary ◽  
Alireza Zamani Bahabadi
Keyword(s):  
Shadowing Property ◽  
Orbital Shadowing

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

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