Lagrangian descriptors for open maps

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 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.

7 pages, 10 figures

References in corpus (17)

• Ray and wave chaos in asymmetric resonant optical cavities
• Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems
• Distinguished trajectories in time dependent vector fields
• Lagrangian Descriptors for Two Dimensional, Area Preserving, Autonomous and Nonautonomous Maps
• Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
• Resonances in open quantum maps
• Localization of resonance eigenfunctions on quantum repellers
• Quantum chaotic resonances from short periodic orbits
• The chaotic set and the cross section for chaotic scattering beyond in 3 degrees of freedom
• Short periodic orbit approach to resonances and the fractal Weyl law
• The Chaotic Saddle in the Lozi map, autonomous and non-autonomous versions
• Structure of resonance eigenfunctions for chaotic systems with partial escape
• Low-dimensional paradigms for high-dimensional hetero-chaos
• Short periodic orbits theory for partially open quantum maps
• Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautomous Henon Map
• Classical transients and the support of open quantum maps
• The role of short periodic orbits in quantum maps with continuous openings

Cited by in corpus (6)

• Quantifying chaos using Lagrangian descriptors
• Visualizing the Phase Space of the HeI_2 van der Waals Complex using Lagrangian Descriptors
• Unveiling the Fractal Structure of Julia Sets with Lagrangian Descriptors
• Geometric parametrisation of Lagrangian Descriptors for 1 degree-of-freedom systems
• Lagrangian descriptors for the Bunimovich stadium billiard
• Identification of the invariant manifolds of the LiCN molecule using Lagrangian descriptors