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Coexistence Phenomena in the Henon Family
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2023 (English)In: Bulletin of the Brazilian Mathematical Society, ISSN 1678-7544, E-ISSN 1678-7714, Vol. 54, no 3, article id 42Article in journal (Refereed) Published
Abstract [en]

We study the classical H & eacute;non family fa,b : (x, y) i? (1 - ax(2) + y, bx), 0 < a < 2, 0 < b < 1, and prove that given an integer k = 1, there is a set of parameters Ek of positive two-dimensional Lebesgue measure so that fa,b, for (a, b) ? E-k, has at least k attractive periodic orbits and one strange attractor of the type studied in Benedicks and Carleson (Ann Math (2) 133(1):73-169, 1991). A corresponding statement also holds for the H & eacute;non-like families of Mora and Viana (Acta Math 171:1-71, 1993), and we use the techniques of Mora and Viana (1993) to study homoclinic unfoldings also in the case of the original H & eacute;non maps. The final main result of the paper is the existence, within the classical H & eacute;non family, of a positive Lebesgue measure set of parameters whose corresponding maps have two coexisting strange attractors.

Place, publisher, year, edition, pages
Springer Nature , 2023. Vol. 54, no 3, article id 42
Keywords [en]
Dynamical systems, Attractors, Henon maps
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-333734DOI: 10.1007/s00574-023-00345-9ISI: 001032491900001Scopus ID: 2-s2.0-85165245332OAI: oai:DiVA.org:kth-333734DiVA, id: diva2:1786896
Note

QC 20230810

Available from: 2023-08-10 Created: 2023-08-10 Last updated: 2023-08-10Bibliographically approved

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Benedicks, MichaelPalmisano, Liviana

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