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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Dynamical trapping in the area-preserving Henon map

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Martins de Oliveira, Vitor [1] ; Ciro, David [2] ; Caldas, Ibere Luiz [1]
Total Authors: 3
[1] Univ Sao Paulo, Inst Fis, Sao Paulo, SP - Brazil
[2] Univ Sao Paulo, Inst Astron Geofis & Ciencias Atmosfer, Sao Paulo, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: European Physical Journal-Special Topics; v. 229, n. 8, SI, p. 1507-1516, MAY 2020.
Web of Science Citations: 1

Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this case, it leads to a temporary trapping of orbits in certain regions of phase space. In this work, we propose that the different scenarios of dynamical trapping can be explained by analyzing the crossings between invariant manifolds. In order to corroborate this assertion, we use an adaptive refinement procedure to approximately obtain the sets of homoclinic and heteroclinic intersections for the area-preserving Henon map, an archetype of open systems, for a generic parameter interval. We show that these sets have very different statistical properties when the system is highly influenced by dynamical trapping, whereas they present similar properties when stickiness is almost absent. We explain these different scenarios by taking into consideration various effects that occur simultaneously in the system, all of which are connected with the topology of the invariant manifolds. (AU)

FAPESP's process: 18/03211-6 - Non linear dynamics
Grantee:Iberê Luiz Caldas
Support type: Research Projects - Thematic Grants