Global dynamics and bifurcation of periodic orbits in a modified Nosé-Hoover oscillator
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Messias, Marcelo (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil))
Reinol, Alisson C. (Universidade Tecnológica Federal do Paraná. Departamento Acadêmico de Matemática (Brazil))

Date:	2020
Abstract:	We perform a global dynamical analysis of a modified Nosé-Hoover oscillator, obtained as the perturbation of an integrable differential system. Using this new approach for studying such an oscillator, in the integrable cases, we give a complete description of the solutions in the phase space, including the dynamics at infinity via the Poincaré compactification. Then using the averaging theory, we prove analytically the existence of a linearly stable periodic orbit which bifurcates from one of the infinite periodic orbits which exist in the integrable cases. Moreover, by a detailed numerical study, we show the existence of nested invariant tori around the bifurcating periodic orbit. Finally, starting with the integrable cases and increasing the parameter values, we show that chaotic dynamics may occur, due to the break of such an invariant tori, leading to the creation of chaotic seas surrounding regular regions in the phase space.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Nosé-Hoover oscillator ; First integral ; Periodic orbit ; Averaging theory ; Invariant tori ; Chaotic dynamics
Published in:	Journal of Dynamical and Control Systems, vol. 17 (June 2020) p. 491-506, ISSN 1573-8698

DOI: 10.1007/s10883-020-09491-5

Postprint 17 p, 1.6 MB

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