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)

Data:	2019
Resum:	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.
Ajuts:	Ministerio de Economía y Competitividad DPI2016-77407-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-388
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Boros-Moll map ; Chaotic set ; Critical line ; Homoclinic bifurcation ; Noninvertible planar map ; Snapback repellor
Publicat a:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 29, Núm. 4 (April 2019) , art. 1930009, ISSN 1793-6551

DOI: 10.1142/S021812741930009X

Postprint 20 p, 1.7 MB

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