Symplectic diffeomorphisms with limit shadowing

2016 ◽  
Vol 10 (02) ◽  
pp. 1750068
Author(s):  
Manseob Lee
Keyword(s):  
Riemannian Manifold ◽  
Closed Formula ◽  
Shadowing Property ◽  
Symplectic Diffeomorphisms ◽  
Limit Shadowing ◽  
Symplectic Diffeomorphism ◽  
Weak Shadowing

Let [Formula: see text] be a symplectic diffeomorphism on a closed [Formula: see text][Formula: see text]-dimensional Riemannian manifold [Formula: see text]. In this paper, we show that [Formula: see text] is Anosov if any of the following statements holds: [Formula: see text] belongs to the [Formula: see text]-interior of the set of symplectic diffeomorphisms satisfying the limit shadowing property or [Formula: see text] belongs to the [Formula: see text]-interior of the set of symplectic diffeomorphisms satisfying the limit weak shadowing property or [Formula: see text] belongs to the [Formula: see text]-interior of the set of symplectic diffeomorphisms satisfying the s-limit shadowing property.

Measure expansive symplectic diffeomorphisms and Hamiltonian systems

2016 ◽  
Vol 27 (09) ◽  
pp. 1650077
Author(s):  
Manseob Lee ◽  
Junmi Park
Keyword(s):  
Riemannian Manifold ◽  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Symplectic Form ◽  
Symplectic Diffeomorphisms ◽  
Symplectic Diffeomorphism

Let [Formula: see text] be a [Formula: see text]-dimensional ([Formula: see text]), compact smooth Riemannian manifold endowed with a symplectic form [Formula: see text]. In this paper, we show that, if a symplectic diffeomorphism [Formula: see text] is [Formula: see text]-robustly measure expansive, then it is Anosov and a [Formula: see text] generic measure expansive symplectic diffeomorphism [Formula: see text] is mixing Anosov. Moreover, for a Hamiltonian systems, if a Hamiltonian system [Formula: see text] is robustly measure expansive, then [Formula: see text] is Anosov.

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.

Diffeomorphisms with thes-limit shadowing property

2012 ◽  
Vol 27 (4) ◽  
pp. 403-410 ◽  
Author(s):  
Kazuhiro Sakai
Keyword(s):  
Shadowing Property ◽  
Limit Shadowing

scholarly journals G-Expansibility and G-Almost Periodic Point under Topological Group Action

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Zhanjiang Ji
Keyword(s):  
Topological Group ◽  
Periodic Point ◽  
Inverse Limit ◽  
The Self ◽  
Almost Periodic ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Shift Map ◽  
Inverse Limit Space ◽  
Almost Periodic Point

Firstly, the new concepts of G − expansibility, G − almost periodic point, and G − limit shadowing property were introduced according to the concepts of expansibility, almost periodic point, and limit shadowing property in this paper. Secondly, we studied their dynamical relationship between the self-map f and the shift map σ in the inverse limit space under topological group action. The following new results are obtained. Let X , d be a metric G − space and X f , G ¯ ,   d ¯ , σ be the inverse limit space of X , G , d , f . (1) If the map f : X ⟶ X is an equivalent map, then we have A P G ¯ σ = Lim ← A p G f , f . (2) If the map f : X ⟶ X is an equivalent surjection, then the self-map f is G − expansive if and only if the shift map σ is G ¯ − expansive. (3) If the map f : X ⟶ X is an equivalent surjection, then the self-map f has G − limit shadowing property if and only if the shift map σ has G ¯ − limit shadowing property. The conclusions of this paper generalize the corresponding results given in the study by Li, Niu, and Liang and Li . Most importantly, it provided the theoretical basis and scientific foundation for the application of tracking property in computational mathematics and biological mathematics.

scholarly journals On Extended Branciari b -Distance Spaces and Applications to Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Reena Jain ◽  
Hemant Kumar Nashine ◽  
Reny George ◽  
Zoran D. Mitrović
Keyword(s):  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Weak Limit ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Shadowing Property ◽  
Underlying Space ◽  
Limit Shadowing ◽  
Fractional Differential ◽  
Well Posed

In this work, we define new α − λ -rational contractive conditions and establish fixed-points results based on aforesaid contractive conditions for a mapping in extended Branciari b -distance spaces. We furnish two examples to justify the work. Further, we discuss results on weak well-posed property, weak limit shadowing property, and generalized w -Ulam-Hyers stability in the underlying space. Finally, as an application of our main result, we obtain sufficient conditions for the existence of solutions of a nonlinear fractional differential equation with integral boundary conditions.

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.

On the theory of fixed point theorems for convex contraction mappings

2015 ◽  
Vol 31 (3) ◽  
pp. 365-371
Author(s):  
VIORICA MURESAN ◽  
◽  
ANTON S. MURESAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Shadowing Property ◽  
Contraction Mappings ◽  
Limit Shadowing

Based on the concepts and problems introduced in [Rus, I. A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541–559], in the present paper we consider the theory of some fixed point theorems for convex contraction mappings. We give some results on the following aspects: data dependence of fixed points; sequences of operators and fixed points; well-posedness of a fixed point problem; limit shadowing property and Ulam-Hyers stability for fixed point equations.

Limit shadowing property

1997 ◽  
Vol 18 (1-2) ◽  
pp. 75-92 ◽  
Author(s):  
Timeo Eirola ◽  
Olvai Nevanlinna ◽  
Sergei Yu Pilyugin
Keyword(s):  
Shadowing Property ◽  
Limit Shadowing
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