Efficient manifolds tracing for planar maps

Autor(es)

Ciro, David ^{[1, 2]} ; Caldas, Ibere L. ^[2] ; Viana, Ricardo L. ^[1] ; Evans, Todd E. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Parana, Dept Phys, BR-81531990 Curitiba, Parana - Brazil

^[2] Univ Sao Paulo, Dept Appl Phys, BR-05508090 Sao Paulo, SP - Brazil

^[3] Gen Atom, POB 85608, San Diego, CA 92186 - USA

• Tipo de documento: Artigo Científico
• Fonte: Chaos; v. 28, n. 9 SEP 2018.
• Citações Web of Science: 0

Resumo

In this work, we introduce an exact calculation method and an approximation technique for tracing the invariant manifolds of unstable periodic orbits of planar maps. The exact method relies on an adaptive refinement procedure that prevents redundant calculations occurring in other approaches, and the approximated method relies on a novel interpolation approach based on normal displacement functions. The resulting approximated manifold is precise when compared to the exact one, and its relative computational cost falls like the inverse of the manifold length. To present the tracing method, we obtain the invariant manifolds of the Chirikov-Taylor map, and as an application we illustrate the transition from homoclinic to heteroclinic chaos in the Duffing oscillator that leads from localized chaos to global chaotic motion. Published by AIP Publishing. (AU)

• Processo FAPESP: 11/19296-1 - Dinâmica não linear
• Beneficiário: Iberê Luiz Caldas
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 12/18073-1 - Transporte simplético em plasmas de fusão com divertor
• Beneficiário: David Ciro Taborda
• Modalidade de apoio: Bolsas no Brasil - Doutorado