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Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies

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Author(s): Lázaro Ochoa, José Tomás; Delshams Valdés, Amadeu; Gonchenko, Marina; Gonchenko, Sergey
Source:
Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Articles publicats en revistes (Matemàtiques i Informàtica)
Dipòsit Digital de la UB
Subject Terms:
Differential equations; Àrees temàtiques de la UPC::Matemàtiques i estadística; Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory; Classificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spaces; 34 Ordinary differential equations::34G Differential equations in abstract spaces [Classificació AMS]; 37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory [Classificació AMS]; Matemàtiques i estadística [Àrees temàtiques de la UPC]; Equacions diferencials; Sistemes dinàmics diferenciables; Dynamics; Sistemes dinàmics; reversible mixed dynamics; Bifurcation theory; Differentiable dynamical systems; Equacions diferencials ordinàries; Teoria de la bifurcació; Newhouse phenomenon; Ordinary differential equations; homoclinic and heteroclinic tangencies
Document Type:
Article
Online Access:
http://hdl.handle.net/2117/121505
http://hdl.handle.net/2445/194449
https://hdl.handle.net/2117/121505
https://doi.org/10.3934/dcds.2018196

Additional Information
- Contributors:
  Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
- Publication Information:
  American Institute of Mathematical Sciences (AIMS), 2018.
- Publication Date:
  2018
- Abstract:
  We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider one-parameter families of reversible maps unfolding the initial homoclinic tangency and prove the existence of infinitely many sequences (cascades) of bifurcations related to the birth of asymptotically stable, unstable and elliptic periodic orbits.
- File Description:
  application/pdf
- Accession Number:
  10.3934/dcds.2018196
- Rights:
  CC BY NC ND
- Accession Number:
  edsair.dedup.wf.002..a60b1730db91187b24e5ec20307fe72a

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