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DIBLÍK, J. CALAMAI, A. FRANCA, M. POSPÍŠIL, M.
Original Title
On the Position of Chaotic Trajectories
Type
journal article in Web of Science
Language
English
Original Abstract
The main purpose of this paper is to locate trajectories of a perturbed system, which is known to behave chaotically. The unperturbed system is assumed to have the origin as a hyperbolic fixed point, and to admit a trajectory homoclinic to the origin. This homocline is assumed to lie in a prescribed region having the origin in its border. Using a Mel’nikov type approach, we introduce natural conditions ensuring that all the chaotic trajectories of the perturbed system, given by classical results, lie in the same region. The applicability of our results is illustrated in two examples. In the first one, we find positive radial solutions for a class of P.D.E.’s, obtaining new results in the case of critical equations ruled by Laplacian with Hardy potentials. In the other one, we show that under certain conditions one of two weakly coupled pendula moves in one direction only.
Keywords
Chaotic behaviour; Hardy potential;· Bernoulli shift; Mel’nikov integral
Authors
DIBLÍK, J.; CALAMAI, A.; FRANCA, M.; POSPÍŠIL, M.
Released
1. 12. 2017
Publisher
Springer
ISBN
1040-7294
Periodical
Journal of Dynamics and Differential Equations
Year of study
29
Number
4
State
United States of America
Pages from
1423
Pages to
1458
Pages count
36
URL
https://link.springer.com/article/10.1007/s10884-016-9520-z
BibTex
@article{BUT142523, author="Alessandro {Calamai} and Josef {Diblík} and Matteo {Franca} and Michal {Pospíšil}", title="On the Position of Chaotic Trajectories", journal="Journal of Dynamics and Differential Equations", year="2017", volume="29", number="4", pages="1423--1458", doi="10.1007/s10884-016-9520-z", issn="1040-7294", url="https://link.springer.com/article/10.1007/s10884-016-9520-z" }