Detail publikace

On the Position of Chaotic Trajectories

Originální název

On the Position of Chaotic Trajectories

Anglický název

On the Position of Chaotic Trajectories

Jazyk

en

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.

BibTex


@article{BUT142523,
  author="Alessandro {Calamai} and Josef {Diblík} and Matteo {Franca} and Michal {Pospíšil}",
  title="On the Position of Chaotic Trajectories",
  annote="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.",
  address="Springer",
  chapter="142523",
  doi="10.1007/s10884-016-9520-z",
  howpublished="print",
  institution="Springer",
  number="4",
  volume="29",
  year="2017",
  month="december",
  pages="1423--1458",
  publisher="Springer",
  type="journal article in Web of Science"
}