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2013
Impact Factor

Antonio Ureña

Dep Matematica Aplicada, UGR, 18071 Granada, Spain
Universidad de Granada

Publications:

Ureña A. J.
The Spectrum of Reversible Minimizers
2018, vol. 23, no. 3, pp.  248-256
Abstract
Poincaré and, later on, Carathéodory, showed that the Floquet multipliers of 1-dimensional periodic curves minimizing the Lagrangian action are real and positive. Even though Carathéodory himself observed that this result loses its validity in the general higherdimensional case, we shall show that it remains true for systems which are reversible in time. In this way, we also generalize a previous result by Offin on the hyperbolicity of nondegenerate symmetric minimizers. Our arguments rely on the higher-dimensional generalizations of the Sturm theory which were developed during the second half of the twentieth century by several authors, including Hartman, Morse or Arnol’d.
Keywords: action minimizers, Floquet multipliers, time reversibility
Citation: Ureña A. J.,  The Spectrum of Reversible Minimizers, Regular and Chaotic Dynamics, 2018, vol. 23, no. 3, pp. 248-256
DOI:10.1134/S1560354718030024

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