Related papers: Global dynamics visualisation from Lagrangian Desc…
This manuscript studies the unsupervised change point detection problem in time series of graphs using a decoder-only latent space model. The proposed framework consists of learnable prior distributions for low-dimensional graph…
Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the…
The identification of invariant objects and Lagrangian coherent structures is a cornerstone of dynamical systems. As a consequence, several diagnostic indicators have been established over time, such as the fast Lyapunov indicator, the…
An important point in analysing the dynamics of a given stellar or planetary system is the reliable identification of the chaotic or regular behaviour of its orbits. We introduce here the program LP-VIcode, a fully operational code which…
The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…
Human mobility, enabled by diverse transportation modes, is fundamental to urban functionality. Studying these movements across scales-from microscopic to macroscopic-yields valuable insights into urban dynamics. Local adaptation and…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
The aim of this research work is to compare the reliability of several variational indicators of chaos on mappings. The Lyapunov Indicator (LI); the Mean Exponential Growth factor of Nearby Orbits (MEGNO); the Smaller Alignment Index…
Understanding the dynamics of multi--dimensional conservative dynamical systems (Hamiltonian flows or symplectic maps) is a fundamental issue of non-linear science. The Generalized ALignment Index (GALI), which was recently introduced and…
This paper proposes an integration of surrogate modeling and topology to significantly reduce the amount of data required to describe the underlying global dynamics of robot controllers, including closed-box ones. A Gaussian Process (GP),…
Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…
Mixed quantum-classical models have been proposed in several contexts to overcome the computational challenges of fully quantum approaches. However, current models typically suffer from long-standing consistency issues, and, in some cases,…
We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field…
In a smooth flow, the leading-order response of trajectories to infinitesimal perturbations in their initial conditions is described by the finite-time Lyapunov exponents and associated characteristic directions of stretching. We give a…
The Lagrangian derivatives of finite-time Lyapunov exponents and the corresponding characteristic directions are shown to satisfy time-asymptotic differential constraints in chaotic flows. The constraints are valid for any metric tensor,…
In this paper we obtain the global dynamics and phase portraits of quadratic and cubic quasi-homogeneous but non-homogeneous systems. We first prove that all planar quadratic and cubic quasi-homogeneous but non-homogeneous polynomial…