An Extension of Discrete Lagrangian Descriptors for Unbounded Maps
Abstract
In this paper, we provide an extension for the method of Discrete Lagrangian Descriptors with the purpose of exploring the phase space of unbounded maps. The key idea is to construct a working definition, that is built on the original approach introduced in [ Lopesino et al., 2015a ], and which relies on stopping the iteration of initial conditions when their orbits leave a certain region in the plane. This criterion is partly inspired by the classical analysis used in Dynamical Systems Theory to study the dynamics of maps by means of escape time plots. We illustrate the capability of this technique to reveal the geometrical template of stable and unstable invariant manifolds in phase space, and also the intricate structure of chaotic sets and strange attractors, by applying it to unveil the phase space of a well-known discrete-time system, the Hénon map.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 01, 2020
- Source ID
- 10.1142/s0218127420300128
Entities
People
- Víctor J. García-garrido
Organizations
- Engineering and Physical Sciences Research Council
- Office of Naval Research
- University of Alcalá