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Horseshoes, Entropy, Homoclinic Trajectories, and Lyapunov Stability
horseshoe, the positivity of topological entropy, the existence of a homoclinic of graph maps, the existence of an arc horseshoe implies the positivity of topological entropy, but we construct a continuous map on ...
BA - Obecná matematika
- 2014 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites
It is known that the positiveness of topological entropy, the existence of a horseshoe and the existence of a homoclinic trajectory are mutually equivalent different definitions of a horseshoe and two different definitions ...
BA - Obecná matematika
- 2011 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Quasi-graphs, zero entropy and measures with discrete spectrum
-graph map with zero topological entropy has discrete spectrum. Additionally, we obtain an analog of Llibre-Misiurewicz's result relating positive topological entropy with existence of topological horseshoes. We al...
Pure mathematics
- 2022 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
Chaos on one-dimensional compact metric spaces
We consider various kinds of chaotic behavior of continuous maps on compact metric spaces: the positivity of topological entropy, the existence of a horseshoe, the existence of a homoclinic trajectory (or perhaps, an eventually peri...
BA - Obecná matematika
- 2012 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
Counterexamples of continuous maps on dendrites
We take a list of properties of continuous maps on compact metric spaces, e.g. the existence of an arc horseshoe, the positivity of topological entropy, the existence of a homoclinic trajectory, the existence of an omega-limit set c...
BA - Obecná matematika
- 2016 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
The Topological Entropy of Banach Spaces
We investigate some properties of (universal) Banach spaces of real functions in the context of topological entropy. Among other things, we show that any subspace of C topological entropy. Also, for any t [0,infinity], we construct ...
BA - Obecná matematika
- 2012 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
Constant slope, entropy, and horseshoes for a map on a tame graph
slope e(htop(f)), where e(htop(f))is the topological entropy of f. Moreover, we show that in our class the topological entropy e(htop(f)) is achievable through horseshoes......
Pure mathematics
- 2020 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
Omega-limit sets and invariant chaos in dimension one
that for a continuous graph map properties positive topological entropy; horseshoe; invariant Li chaos is weaker than positive topological entropy. The equivalency arises when we......
BA - Obecná matematika
- 2016 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
Properties of Dynamical Systems on Dendrites and Graphs
In this paper, we consider fourteen dynamical properties, provide new results and survey all the relations among the properties for the case of graph maps and all known relations for the case of dendrite maps....
Pure mathematics
- 2021 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
Topological entropy of composition and impulsive differential equations satisfying a uniqueness condition
The impulsive differential equations are examined via the associated Poincaré translation operators in terms of topological entropy. The crucial role is played obtained by means of horseshoes. For the vector (higher-dimensional) pro...
Pure mathematics
- 2022 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
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