Related papers: Effective symbolic dynamics, random points, statis…
The ordinal approach to evaluate time series due to innovative works of Bandt and Pompe has increasingly established itself among other techniques of nonlinear time series analysis. In this paper, we summarize and generalize the theory of…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be modeled as classical systems of particles interacting with short range, repulsive forces. Here we give a…
The Kolmogorov-Sinai (K-S) entropy is a central measure of complexity and chaos. Its calculation for many-body systems is an interesting and important challenge. In this paper, the evaluation is formulated by considering $N$-dimensional…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods,…
The periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics. The corresponding partition is mapped to a topological well-ordered symbol plane. In the symbol plane the pruning front is…
Symbolic systems are powerful frameworks for modeling cognitive processes as they encapsulate the rules and relationships fundamental to many aspects of human reasoning and behavior. Central to these models are systematicity,…
The spatial character of territorial systems plays a crucial role in the emergence of their complexities. This contribution aims at illustrating to what extent different types of complexities can be exhibited in models of such systems. We…
Three topics in dynamical systems are discussed. In the first two sections we solve some open problems concerning, respectively, Furstenberg entropy of stationary dynamical systems, and uniformly rigid actions admitting a weakly mixing…
We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space,…
We describe the statistical properties of the dynamics of the quadratic polynomials P_a(z):=e^{2\pi a i} z+z^2 on the complex plane, with a of high return times. In particular, we show that these maps are uniquely ergodic on their measure…
It is known that unstable periodic orbits of a given map give information about the natural measure of a chaotic attractor. In this work we show how these orbits can be used to calculate the density function of the first Poincar\'e returns.…
The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge…
Pesin's formula relates the entropy of a dynamical system with its positive Lyapunov exponents. It is well known, that this formula holds true for random dynamical systems on a compact Riemannian manifold with invariant probability measure…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms…
New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with ``flights'',…
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…