相关论文: Shortest distance between multiple orbits and gene…
The escape dynamics in a two-dimensional multiwell potential is explored. A thorough numerical investigation is conducted in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra…
We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…
The level statistics of pseudointegrable fractal drums is studied numerically using periodic orbit theory. We find that the spectral rigidity $\Delta_3(L)$, which is a measure for the correlations between the eigenvalues, decreases to quite…
In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system.…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
We relate the entropy of entanglement of ensembles of random vectors to their generalized fractal dimensions. Expanding the von Neumann entropy around its maximum we show that the first order only depends on the participation ratio, while…
Spreading according to simple rules (e.g. of fire or diseases), and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (``Small-World'' lattices). The volume V(t) covered…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
We investigate the distributions of the orbital period ratios of adjacent planets in high multiplicity \kepler\ systems (four or more planets) and low multiplicity systems (two planets). Modeling the low multiplicity sample as essentially…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
The dynamical Mordell-Lang conjecture concerns the structure of the intersection of an orbit in an algebraic dynamical system and an algebraic variety. In this paper, we bound the size of this intersection for various cases when it is…
The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications.…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
A discussion about dependences of the (fractal) basin boundary dimension with the definition of the basins and the size of the exits is presented for systems with one or more exits. In particular, it is shown that the dimension is largely…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
The exchange of "information" between a system and its environment based on the reduced dynamics is investigated. The association of trace distance with information cannot be stated, because of lack of symmetry between leakage from the…
A deep-space exploration mission with low-thrust propulsion to rendezvous with multiple asteroids is investigated. Indirect methods, based on the optimal control theory, are implemented to optimize the fuel consumption. The application of…