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.

CALAMAI, A., Diblík, J., FRANCA, M., Pospíšil, M. (2017). On the position of chaotic trajectories. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 29(4), 1423-1458 [10.1007/s10884-016-9520-z].

On the position of chaotic trajectories

FRANCA, Matteo
Membro del Collaboration Group
;
2017

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.
2017
CALAMAI, A., Diblík, J., FRANCA, M., Pospíšil, M. (2017). On the position of chaotic trajectories. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 29(4), 1423-1458 [10.1007/s10884-016-9520-z].
CALAMAI, Alessandro; Diblík, J.; FRANCA, Matteo; Pospíšil, M.
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/721110
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact