相关论文: Orbit complexity, initial data sensitivity and wea…
We apply to bidimensional chaotic maps the numerical method proposed by Ginelli et al. to approximate the associated Oseledets splitting, i.e. the set of linear subspaces spanned by the so called covariant Lyapunov vectors (CLV) and…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
Perturbative approaches are methods to efficiently tackle many-body problems, offering both intuitive insights and analysis of correlation effects. However, their application to systems where light and matter are strongly coupled is…
The fundamental theorem of classical optimal transport establishes strong duality and characterizes optimizers through a complementary slackness condition. Milestones such as Brenier's theorem and the Kantorovich-Rubinstein formula are…
We introduce a notion of sensitivity, with respect to a continuous bounded observable, which provides a sufficient condition for a continuous map, acting on a Baire metric space, to exhibit a Baire generic subset of points with historic…
We extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the…
Various kinematical quantities associated with the statistical properties of dynamical systems are examined: statistics of the motion, dynamical bases and Lyapunov exponents. Markov partitons for chaotic systems, without any attempt at…
The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the…
This work develops an operator-theoretic and dynamical framework inspired by the Riemann--von Mangoldt formula, chaotic dynamics, and random-matrix models for the Riemann zeta function, without attempting to prove the Riemann Hypothesis.…
We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a…
We review the notion of reducibility and we introduce and discuss the notion of orbital reducibility for autonomous ordinary differential equations of first order. The relation between (orbital) reducibility and (orbital) symmetry is…
We consider the dynamical behavior of Martin-L\"of random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic…
The case of the classical Hill problem is numerically investigated by performing a thorough and systematic classification of the initial conditions of the orbits. More precisely, the initial conditions of the orbits are classified into four…
The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and…
In recent years, statistical characterization of the discrete conservative dynamical systems (more precisely, paradigmatic examples of area-preserving maps such as the standard and the web maps) has been analyzed extensively and shown that,…
Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a…
Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifested in reference to the existence of relativistic flows, related in turn to the production of intense electric fields in magnetized systems.…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…
The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modeled in the context of the pseudo-Newtonian circular restricted three-body problem, such that…
We study the statistical properties of Lanczos coefficients over an ensemble of random initial operators generating the Krylov space. We propose two statistical quantities that are important in characterizing the complexity: the average…