On the Position of Chaotic Trajectories

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26620%2F17%3APU125855" target="_blank" >RIV/00216305:26620/17:PU125855 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10884-016-9520-z" target="_blank" >https://link.springer.com/article/10.1007/s10884-016-9520-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10884-016-9520-z" target="_blank" >10.1007/s10884-016-9520-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Position of Chaotic Trajectories

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the Position of Chaotic Trajectories

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/ED1.1.00%2F02.0068" target="_blank" >ED1.1.00/02.0068: CEITEC - central european institute of technology</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Dynamics and Differential Equations

ISSN

1040-7294

e-ISSN

1572-9222

Svazek periodika

29

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

36

Strana od-do

1423-1458

Kód UT WoS článku

000415618400009

EID výsledku v databázi Scopus

2-s2.0-84958767311