Lagrangian descriptors for open maps

Gabriel G. Carlo and F. Borondo
Phys. Rev. E 101, 022208 – Published 14 February 2020

Abstract

We adapt the concept of Lagrangian descriptors, which have been recently introduced as efficient indicators of phase space structures in chaotic systems, to unveil the key features of open maps. We apply them to the open tribaker map, a paradigmatic example not only in classical but also in quantum chaos. Our definition allows us to identify in a very simple way the inner structure of the chaotic repeller, which is the fundamental invariant set that governs the dynamics of this system. The homoclinic tangles of periodic orbits (POs) that belong to this set are clearly found. This could also have important consequences for chaotic scattering and in the development of the semiclassical theory of short POs for open systems.

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  • Received 23 October 2019
  • Accepted 27 January 2020

DOI:https://doi.org/10.1103/PhysRevE.101.022208

©2020 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

Gabriel G. Carlo1,* and F. Borondo2,3,†

  • 1Comisión Nacional de Energía Atómica, CONICET, Departamento de Física, Av. del Libertador 8250, 1429 Buenos Aires, Argentina
  • 2Departamento de Química, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
  • 3Instituto de Ciencias Matemáticas (ICMAT), Cantoblanco, 28049 Madrid, Spain

  • *carlo@tandar.cnea.gov.ar
  • f.borondo@uam.es

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Vol. 101, Iss. 2 — February 2020

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