Horseshoes, Entropy, Homoclinic Trajectories, and Lyapunov Stability

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F14%3A%230000412" target="_blank" >RIV/47813059:19610/14:#0000412 - isvavai.cz</a>
Result on the web
<a href="http://www.worldscientific.com/doi/abs/10.1142/S0218127414500163" target="_blank" >http://www.worldscientific.com/doi/abs/10.1142/S0218127414500163</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218127414500163" target="_blank" >10.1142/S0218127414500163</a>

Result language
angličtina
Original language name
Horseshoes, Entropy, Homoclinic Trajectories, and Lyapunov Stability
Original language description
We consider six properties of continuous maps, such as the existence of an arc horseshoe, the positivity of topological entropy, the existence of a homoclinic trajectory, or Lyapunov instability on the set of periodic points. The relations between the considered properties are provided in the case of graph maps, dendrite maps and maps on compact metric spaces. For example, by [Llibre & Misiurewicz, 1993] in the case of graph maps, the existence of an arc horseshoe implies the positivity of topological entropy, but we construct a continuous map on a Peano continuum with an arc horseshoe and zero topological entropy. We also formulate one open problem.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP201%2F10%2F0887" target="_blank" >GAP201/10/0887: Discrete dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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