• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.929-942
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• 2023

In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(IFS) on uniform spaces. We show that an IFS on a sequentially compact uniform space with topological ergodic shadowing property has topological shadowing property. We define the notion of topological pseudo-orbital specification property and investigate its relation to topological ergodic shadowing property. We find that a topologically mixing IFS on a compact and sequentially compact uniform space with topological shadowing property has topological pseudo-orbital specification property and thus has topological ergodic shadowing property.

• 대한수학회보
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• 제53권2호
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• pp.581-588
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• 2016

Komuro [3] proved that geometric Lorentz attractor does not satisfy the shadowing property. In this paper we study the condition under which geometric Lorenz attractor has the orbital shadowing property that is weaker than the shadowing property.

• 대한수학회보
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• 제45권4호
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• pp.645-650
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• 2008

Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the $C^0$ topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W.

• 충청수학회지
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• 제25권4호
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• pp.739-745
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• 2012

We show that if a symplectic diffeomorphism has the $C^1$-robustly orbital shadowing property, then the diffeomorphism is Anosov.

• 대한수학회지
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• 제45권6호
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• pp.1505-1521
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• 2008

In this paper, we give a characterization of the structurally stable vector fields via the notion of orbital inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of $C^1$ vector fields with the orbital inverse shadowing property coincides with the set of structurally stable vector fields. This fact improves the main result obtained by K. Moriyasu et al. in [15].

• 대한수학회논문집
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• 제21권3호
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• pp.515-526
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• 2006

In this paper, we give a characterization of hyperbolic linear dynamical systems via the notions of various inverse shadowing. More precisely it is proved that for a linear dynamical system f(x)=Ax of ${\mathbb{C}^n}$, f has the ${\tau}_h$ inverse(${\tau}_h-orbital$ inverse or ${\tau}_h-weak$ inverse) shadowing property if and only if the matrix A is hyperbolic.

• 대한수학회보
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• 제59권2호
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• pp.319-343
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• 2022

We discuss the notions of positive expansivity, chain transitivity, uniform rigidity, chain mixing, weak specification, and pseudo orbital specification in terms of finite open covers for Hausdorff topological spaces and entourages for uniform spaces. We show that the two definitions for each notion are equivalent in compact Hausdorff spaces and further they are equivalent to their standard definitions in compact metric spaces. We show that a homeomorphism on a Hausdorff uniform space has uniform h-shadowing if and only if it has uniform shadowing and its inverse is uniformly equicontinuous. We also show that a Hausdorff positively expansive system with a Hausdorff shadowing property has Hausdorff h-shadowing.