Related papers: An Extension of Discrete Lagrangian Descriptors fo…

In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the…

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…

We present our recent contributions to the theory of Lagrangian descriptors for discriminating ordered and deterministic chaotic trajectories. The class of Lagrangian Descriptors we are dealing with is based on the Euclidean length of the…

In this paper we demonstrate the capability of the method of Lagrangian descriptors to unveil the phase space structures that characterize transport in high-dimensional symplectic maps. In order to illustrate its use, we apply it to a…

We study geometry of the phase space for finite-dimensional dynamical systems with degenerate Lagrangians. The Lagrangian and Hamiltonian constraint formalisms are treated as different local-coordinate pictures of the same invariant…

In this paper we generalize the method of Lagrangian descriptors to two dimensional, area preserving, autonomous and nonautonomous discrete time dynamical systems. We consider four generic model problems--a hyperbolic saddle point for a…

Complementary to existing applications of Lagrangian descriptors as an exploratory method, we use Lagrangian descriptors to find invariant manifolds in a system where some invariant structures have already been identified. In this case we…

Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a…

This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…

The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. We propose a novel, direct geometric method to identify subsets of phase space that…

Lagrangian descriptors reveal the dynamical skeleton governing transport mechanisms of a generic flow. In doing so, they unveil geometrical structures in the phase space that separate regions with different qualitative behavior. This work…

This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigourous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for…

Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…

We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They…

Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the…

A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where…

We present the capability of Lagrangian descriptors for revealing the high dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle. These phase space structures include normally…

This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as…