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DC Field | Value | Language |
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dc.contributor.author | Gonchenko, Marina | - |
dc.contributor.author | Kazakov, Alexey O. | - |
dc.contributor.author | Samylina, Evgeniya A. | - |
dc.contributor.author | Shykhmamedov, Aikan | - |
dc.date.accessioned | 2023-02-28T19:37:58Z | - |
dc.date.available | 2023-02-28T19:37:58Z | - |
dc.date.issued | 2022-02-16 | - |
dc.identifier.issn | 1560-3547 | - |
dc.identifier.uri | http://hdl.handle.net/2445/194357 | - |
dc.description.abstract | We consider reversible nonconservative perturbations of the conservative cubic Hénon maps $H^{\pm}_3: \bar x=y, \bar y=−x+M_1+M_2 y \pm y^3$ and study their influence on the 1:3 resonance, i. e., bifurcations of fixed points with eigenvalues $e^{±i2π/3}$. It follows from [1] that this resonance is degenerate for $M_1=0, M_2=−1$ when the corresponding fixed point is elliptic. We show that bifurcations of this point under reversible perturbations give rise to four 3-periodic orbits, two of them are symmetric and conservative (saddles in the case of map $H^+_3$ and elliptic orbits in the case of map $H^−_3$), the other two orbits are nonsymmetric and they compose symmetric couples of dissipative orbits (attracting and repelling orbits in the case of map $H^+_3$ and saddles with the Jacobians less than 1 and greater than 1 in the case of map $H^−_3$). We show that these local symmetry-breaking bifurcations can lead to mixed dynamics due to accompanying global reversible bifurcations of symmetric nontransversal homo- and heteroclinic cycles. We also generalize the results of [1] to the case of the p:q resonances with odd q and show that all of them are also degenerate for the maps $H^\pm_3$ with $M_1=0$. . | - |
dc.format.extent | 19 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Pleiades Publishing | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1134/S1560354722020058 | - |
dc.relation.ispartof | Regular and Chaotic Dynamics, 2022, vol. 27, num. 2, p. 198-216 | - |
dc.relation.uri | https://doi.org/10.1134/S1560354722020058 | - |
dc.rights | (c) Pleiades Publishing, 2022 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Teoria de la bifurcació | - |
dc.subject.classification | Sistemes dinàmics diferenciables | - |
dc.subject.classification | Teoria ergòdica | - |
dc.subject.classification | Sistemes dinàmics diferenciables | - |
dc.subject.other | Bifurcation theory | - |
dc.subject.other | Differentiable dynamical systems | - |
dc.subject.other | Ergodic theory | - |
dc.subject.other | Differentiable dynamical systems | - |
dc.title | On 1:3 Resonance Under Reversible Perturbations of Conservative Cubic Hénon Maps | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 730958 | - |
dc.date.updated | 2023-02-28T19:37:58Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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730958.pdf | 1.03 MB | Adobe PDF | View/Open |
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