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The field of analytic combinatorics, which studies the asymptotic behaviour of sequences through analytic properties of their generating functions, has led to the development of deep and powerful tools with applications across mathematics…
A simple construction is presented, which generalises piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature,…
We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice, with parameters determined by the probability distribution…
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
This article explores some geometric and algebraic properties of the dynamical system which is represented by matrix differential equations arising from inertial navigation problems, such as the symplecticity and the orthogonality.…
We investigate localization phenomena and stability properties of quasiperiodic oscillations in $N$ degree of freedom Hamiltonian systems and $N$ coupled symplectic maps. In particular, we study an example of a parametrically driven…
Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3…
Recently, the theory concerning piecewise smooth vector fields (PSVFs for short) have been undergoing important improvements. In fact, many results obtained do not have an analogous for smooth vector fields. For example, the chaoticity of…
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,…
It is investigated how a spatial quenched disorder modifies the dynamics of coupled map lattices. The disorder is introduced via the presence or absence of coupling terms among lattice sites. Two nonlinear maps have been considered…
In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…
In this paper we study the dynamics and ergodic theory of certain economic models which are implicitly defined. We consider 1-dimensional and 2-dimensional overlapping generations models, a cash-in-advance model, heterogeneous markets and a…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
The work described in this paper can be interpreted as an application of the order patterns of symbolic dynamics when dealing with unimodal maps. Specifically, it is shown how Gray codes can be used to estimate the probability distribution…
We propose a novel classification framework grounded in symbolic dynamics and data compression using chaotic maps. The core idea is to model each class by generating symbolic sequences from thresholded real-valued training data, which are…
A method to predict the emergence of different kinds of ordered collective behaviors in systems of globally coupled chaotic maps is proposed. The method is based on the analogy between globally coupled maps and a map subjected to an…
This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
We explore the chaotic dynamics of a large one-dimensional lattice of coupled maps with diffusive coupling of varying strength using the covariant Lyapunov vectors (CLVs). Using a lattice of diffusively coupled quadratic maps we quantify…