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A Route to Chaos in the Boros-Moll Map
Gardini, Laura (University of Urbino. Department of Economics Society Politics)
Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
Sushko, Iryna (National Academy of Sciences of Ukraine)

Date: 2019
Abstract: The Boros-Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to their convergence. In the paper, we study the dynamics of a one-parameter family of maps which unfold the Boros-Moll one, showing that the existence of an unbounded invariant chaotic region in the Boros-Moll map is a peculiar feature within the family. We relate this singularity with a specific property of the critical lines that occurs only for this special case. In particular, we explain how the unbounded chaotic region in the Boros-Moll map appears. We especially explain the main contact/homoclinic bifurcations that occur in the family. We also report some other bifurcation phenomena that appear in the considered unfolding.
Note: Número d'acord de subvenció MINECO/DPI2016-77407-P
Note: Número d'acord de subvenció AGAUR/2017/SGR-388
Rights: Tots els drets reservats
Language: Anglès.
Document: article ; recerca ; submittedVersion
Subject: Boros–Moll map ; Chaotic set ; Critical line ; Homoclinic bifurcation ; Noninvertible planar map ; Snapback repellor
Published in: International journal of bifurcation and chaos in applied sciences and engineering, Vol. 29, Núm. 4 (April 2019) , art. 1930009, ISSN 0218-1274

DOI: 10.1142/S021812741930009X


Preprint
20 p, 1.7 MB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2019-05-16, last modified 2019-10-14



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