Search

Your search keyword '"Kawaguchi, Noriaki"' showing total 1,337 results
Start Over Author "Kawaguchi, Noriaki"
1,337 results on '"Kawaguchi, Noriaki"'

1. Some results on s-limit shadowing and Li-Yorke type chaos

Author

Kawaguchi, Noriaki

Subjects
Mathematics - Dynamical Systems, 37B05, 37B35, 37B65, 37D45
Abstract

In [13], for any continuous self-map of a compact metric space with s-limit shadowing, by using a $G_\delta$-partition of the phase space, a global description of Li-Yorke type chaos (with respect to several particular Furstenberg families) is obtained. In this paper, we complement the results in [13] by some results concerning the s-limit shadowing and general Furstenberg families. An example is also given to illustrate the results., Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:2308.11163

Published
2024

2. Shadowing and the basins of terminal chain components

Author

Kawaguchi, Noriaki

Subjects
Mathematics - Dynamical Systems, 37B65
Abstract

We provide an alternative view of some results in [1, 3, 11]. In particular, we prove that (1) if a continuous self-map of a compact metric space has the shadowing, then the union of the basins of terminal chain components is a dense $G_\delta$-subset of the space; and (2) if a continuous self-map of a locally connected compact metric space has the shadowing, and if the chain recurrent set is totally disconnected, then the map is almost chain continuous., Comment: 8 pages

Published
2024

3. Contractive shadowing property of dynamical systems

Author

Kawaguchi, Noriaki

Subjects
Mathematics - Dynamical Systems, 37B65
Abstract

For topological dynamical systems defined by continuous self-maps of compact metric spaces, we consider the contractive shadowing property, i.e., the Lipschitz shadowing property such that the Lipschitz constant is less than 1. We prove some basic properties of contractive shadowing and show that non-degenerate homeomorphisms do not have the contractive shadowing property. Then, we consider the case of ultrametric spaces. We also discuss the spectral decomposition of the chain recurrent set under the assumption of contractive shadowing. Several examples are given to illustrate the results., Comment: 21 pages

Published
2023

4. Some results on shadowing and local entropy properties of dynamical systems

Author

Kawaguchi, Noriaki

Subjects
Mathematics - Dynamical Systems, 37B40, 37B65
Abstract

We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give some necessary and sufficient conditions for (non) h-expansiveness under the assumption of shadowing and chain transitivity; and use the result to present a counter-example for a question raised by Artigue et al. [Proc. Amer. Math. Soc. 150 (2022), 3369-3378]., Comment: 22 pages

Published
2023

5. S-limit shadowing and a global description of Li-Yorke type chaos

Author

Kawaguchi, Noriaki

Subjects
Mathematics - Dynamical Systems, 37B05, 37B35, 37B65, 37D45
Abstract

For any continuous self-map of a compact metric space, we extend a partition of each chain component with respect to a chain proximal relation to a $G_\delta$-partition of the phase space. Under the assumption of s-limit shadowing, we use this partition to give a global description of Li-Yorke type chaos corresponding to several Furstenberg families., Comment: 18 pages

Published
2023

6. S-limit shadowing implies the denseness of chain components with the shadowing property

Author

Kawaguchi, Noriaki

Subjects
Mathematics - Dynamical Systems, 37B65
Abstract

For any continuous self-map of a compact metric space, we consider the space of chain components and prove that the s-limit shadowing implies the denseness of chain components with the shadowing property. It gives a partial answer to a question raised by Moothathu [Topology Appl. 158 (2011) 2232--2239]. We also prove that the s-limit shadowing is not generic in the space of homeomorphisms of a closed differentiable manifold., Comment: 8 pages

Published
2023

7. Shadowing, transitivity and a variation of omega-chaos

Author

Kawaguchi, Noriaki

Subjects
Mathematics - Dynamical Systems, 37D45, 37B65
Abstract

We study a special type of shadowing (DSP) of chain transitive continuous self-maps of compact Hausdorff spaces. We prove some basic properties of DSP. As application of DSP, we obtain sufficient conditions for a statistical variant of $\omega$-chaos and prove the topological genericity of it. We also consider topological distribution of irregular points under the assumption of DSP., Comment: 46 pages

Published
2023

38. Generic and dense distributional chaos with shadowing

Author

Kawaguchi, Noriaki

Subjects
Mathematics - Dynamical Systems
Abstract

For continuous self-maps of compact metric spaces, we consider the notions of generic and dense chaos introduced by Lasota and Snoha and their variations for the distributional chaos, under the assumption of shadowing. We give some equivalent properties to generic uniform (distributional) chaos in terms of chains and prove their equivalence to generic (distributional) chaos under the shadowing. Several examples illustrating the main results are also given.

Published
2021

Catalog

Books, media, physical & digital resources
See catalog results