3 citations · 8 across the 14 of their papers we have counts for
14 papers · 1 filter
Shadowing, sensitivity and entropy points
Noriaki Kawaguchi
For continuous self-maps of compact metric spaces, we explore the relationship among the shadowable points, sensitive points, and entropy points. Specifically, we show that (1) if…
Sufficient conditions for distributional chaos of type I
Noriaki Kawaguchi
Distributional chaos of type I (DC1) is a stronger variant of Li-Yorke chaos. In this paper, we consider the fact that the time-one map of a mixing Anosov flow exhibits DC1 and gen…
Shadowing and the basins of terminal chain components
Noriaki Kawaguchi
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…
Contractive shadowing property of dynamical systems
Noriaki Kawaguchi
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 s…
Some results on shadowing and local entropy properties of dynamical systems
Noriaki Kawaguchi
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 poin…
S-limit shadowing and a global description of Li-Yorke type chaos
Noriaki Kawaguchi
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 -partition of the phase spa…
S-limit shadowing implies the denseness of chain components with the shadowing property
Noriaki Kawaguchi
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…
Shadowing, transitivity and a variation of omega-chaos
Noriaki Kawaguchi
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 ob…
Generic and dense distributional chaos with shadowing
Noriaki Kawaguchi
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 cha…
On -genericity of distributional chaos
Noriaki Kawaguchi
Let be a compact smooth manifold without boundary. Based on results by Good and Meddaugh (2020), we prove that a strong distributional chaos is -generic in the space of co…
A type of shadowing and distributional chaos
Noriaki Kawaguchi
For any continuous self-map of a compact metric space, we prove a saturation of distributionally scrambled Mycielski sets under a type of shadowing and the chain transitivity.
Distributionally chaotic maps are -dense
Noriaki Kawaguchi
We prove that the set of maps which exhibit distributional chaos of type 1 (DC1) is -dense in the space of continuous self-maps of given any compact topological manifold (poss…
On the topological stability and shadowing in zero-dimensional spaces
Noriaki Kawaguchi
In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological s…
On the shadowing and limit shadowing properties
Noriaki Kawaguchi
We study the relation between the shadowing property and the limit shadowing property. We prove that if a continuous self-map of a compact metric space has the limit shadowing…