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Lagrangian descriptors for open maps.

Gabriel G Carlo1, F Borondo2,3

  • 1Comisión Nacional de Energía Atómica, CONICET, Departamento de Física, Av. del Libertador 8250, 1429 Buenos Aires, Argentina.

Physical Review. E
|March 15, 2020
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Summary
This summary is machine-generated.

Lagrangian descriptors reveal the structure of chaotic repellers in open maps, like the tribaker map. This method simplifies identifying key dynamical features and periodic orbits in classical and quantum chaos.

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Area of Science:

  • Dynamical systems theory
  • Quantum chaos
  • Statistical mechanics

Background:

  • Lagrangian descriptors are recent tools for analyzing chaotic systems.
  • Open maps present unique challenges in dynamical systems analysis.
  • The tribaker map is a key model in classical and quantum chaos.

Purpose of the Study:

  • To adapt Lagrangian descriptors for analyzing open maps.
  • To identify the fundamental invariant set (chaotic repeller) in open systems.
  • To explore the structure of homoclinic tangles of periodic orbits.

Main Methods:

  • Adaptation of Lagrangian descriptors for open maps.
  • Application to the open tribaker map.
  • Identification of invariant sets and periodic orbits.

Main Results:

  • Successfully identified the inner structure of the chaotic repeller.
  • Clearly detected homoclinic tangles of periodic orbits.
  • Demonstrated the utility of Lagrangian descriptors in open systems.

Conclusions:

  • Lagrangian descriptors offer a simple and effective method for studying open maps.
  • Findings impact understanding of chaotic scattering and semiclassical theories.
  • The approach provides insights into the dynamics of complex systems.