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 Regul. Chaotic Dyn., 2018, Volume 23, Issue 3, Pages 248–256 (Mi rcd321)

The Spectrum of Reversible Minimizers

Antonio J. Ureña

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

 Funding Agency Grant Number Federación Española de Enfermedades Raras MTM2014- 5223 The author is partially supported by Spanish MICINN Grant with FEDER funds MTM2014-5223.

DOI: https://doi.org/10.1134/S1560354718030024

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Bibliographic databases:

MSC: 37J25, 37J50, 34D08
Accepted:17.02.2018
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Citation: Antonio J. Ureña, “The Spectrum of Reversible Minimizers”, Regul. Chaotic Dyn., 23:3 (2018), 248–256

Citation in format AMSBIB
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