Detail publikačního výsledku

On the Position of Chaotic Trajectories

DIBLÍK, J.; CALAMAI, A.; FRANCA, M.; POSPÍŠIL, M.

Originální název

On the Position of Chaotic Trajectories

Anglický název

On the Position of Chaotic Trajectories

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

Chaotic behaviour; Hardy potential;· Bernoulli shift; Mel’nikov integral

Klíčová slova v angličtině

Chaotic behaviour; Hardy potential;· Bernoulli shift; Mel’nikov integral

Autoři

DIBLÍK, J.; CALAMAI, A.; FRANCA, M.; POSPÍŠIL, M.

Rok RIV

2018

Vydáno

01.12.2017

Nakladatel

Springer

ISSN

1040-7294

Periodikum

Journal of Dynamics and Differential Equations

Svazek

29

Číslo

4

Stát

Spojené státy americké

Strany od

1423

Strany do

1458

Strany počet

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"
}