scholarly journals Statistical complexity of the kicked top model considering chaos

2020 ◽  
Vol 12 (2) ◽  
pp. 283-301
Author(s):  
Ágnes Fülöp
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Probability Distribution ◽  
Structural Complexity ◽  
Statistical Complexity ◽  
Kicked Rotor ◽  
Rotor Model

Abstract The concept of the statistical complexity is studied to characterize the classical kicked top model which plays important role in the qbit systems and the chaotic properties of the entanglement. This allow us to understand this driven dynamical system by the probability distribution in phase space to make distinguish among the regular, random and structural complexity on finite simulation. We present the dependence of the kicked top and kicked rotor model through the strength excitation in the framework of statistical complexity.

GENERALIZED STATISTICAL COMPLEXITY MEASURE

2010 ◽  
Vol 20 (03) ◽  
pp. 775-785 ◽  
Author(s):  
OSVALDO A. ROSSO ◽  
LUCIANA DE MICCO ◽  
HILDA A. LARRONDO ◽  
MARÍA T. MARTÍN ◽  
ANGEL PLASTINO
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Probability Distribution ◽  
Metric Space ◽  
Fundamental Problem ◽  
Complexity Measure ◽  
Causal Effects ◽  
Probability Metric ◽  
Statistical Complexity ◽  
Selection Of

A generalized Statistical Complexity Measure (SCM) is a functional that characterizes the probability distribution P associated to the time series generated by a given dynamical system. It quantifies not only randomness but also the presence of correlational structures. We review here several fundamental issues in such a respect, namely, (a) the selection of the information measure [Formula: see text]; (b) the choice of the probability metric space and associated distance [Formula: see text]; (c) the question of defining the so-called generalized disequilibrium [Formula: see text]; (d) the adequate way of picking up the probability distribution P associated to a dynamical system or time series under study, which is indeed a fundamental problem. In this communication we show (point d) that sensible improvements in the final results can be expected if the underlying probability distribution is "extracted" via appropriate consideration regarding causal effects in the system's dynamics.

scholarly journals Statistical complexity and generalized number system

2014 ◽  
Vol 6 (2) ◽  
pp. 230-251 ◽  
Author(s):  
Ágnes Fülöp
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Numerical Approximation ◽  
Structural Complexity ◽  
Number System ◽  
Dynamical Behaviour ◽  
Finite Systems ◽  
Regular Motion ◽  
Statistical Complexity

Abstract We apply the concept of statistical complexity to understand the dynamical behaviour of the time series by the probability distribution. This quantity allows to distinguish between the random, regular motion and the structural complexity in finite systems. We determined the numerical approximation of the statistical complexity of the Lozi attractor and the generalized number system

scholarly journals Statistical complexity of the quasiperiodical damped systems

2018 ◽  
Vol 10 (2) ◽  
pp. 241-256
Author(s):  
Ágnes Fülöp
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Probability Distribution ◽  
Structural Complexity ◽  
Statistical Complexity ◽  
Making A Difference ◽  
Forced Pendulum ◽  
Damped Systems

Abstract We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the time series making a difference between the regular, random and structural complexity on finite measurements. We interpreted the statistical complexity on snapshot attractor and determined it on the quasiperiodical forced pendulum.

scholarly journals A Dynamical System with q-Deformed Phase Space Represented in Ordinary Variable Spaces

2010 ◽  
Vol 124 (6) ◽  
pp. 1019-1035
Author(s):  
S. Naka ◽  
H. Toyoda ◽  
T. Takanashi
Keyword(s):  
Dynamical System ◽  
Phase Space

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

scholarly journals ON BARYON NUMBER NONCONSERVATION IN TWO-DIMENSIONAL O(2N+1) QCD

2010 ◽  
Vol 25 (06) ◽  
pp. 1253-1266
Author(s):  
TAMAR FRIEDMANN
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Matrix Models ◽  
Gauge Group ◽  
Baryon Number ◽  
Two Dimensional ◽  
Infinite Dimensional ◽  
Field Approach ◽  
Large N ◽  
Classical Dynamical System

We construct a classical dynamical system whose phase space is a certain infinite-dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O (2N+1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.

A DYNAMICAL SYSTEM APPROACH TO THE GBIG COSMOLOGY

2011 ◽  
Vol 08 (06) ◽  
pp. 1179-1188 ◽  
Author(s):  
KOUROSH NOZARI ◽  
F. KIANI
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Cosmological Constant ◽  
System Approach ◽  
Stable Solution ◽  
Late Time ◽  
Curvature Effect ◽  
De Sitter ◽  
Dynamical System Approach ◽  
Bonnet Term

We study the phase space of an extension of the normal DGP cosmology with a cosmological constant on the brane and curvature effect that is incorporated via the Gauss–Bonnet term in the bulk action. We study late-time cosmological dynamics of this scenario within a dynamical system approach. We show that the stable solution of the cosmological dynamics in this model is a de Sitter phase.

scholarly journals Bifurcation and anomalous spectral accumulation in an oval billiard

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
Hironori Makino
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Limited Region ◽  
Classical Dynamical System ◽  
Classical Trajectories ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Spectral Statistics ◽  
Math Phys ◽  
Good Agreement

Abstract The spectral statistics of a quantum oval billiard whose classical dynamical system shows bifurcations is numerically investigated in terms of the two-point correlation function (TPCF), which is defined as the probability density of finding two levels at a specific energy interval. The eigenenergy levels at the bifurcation point are found to show anomalous accumulation, which is observed as a periodic spike oscillation of the TPCF. We analyzed the eigenfunctions localizing onto the various classical trajectories in the phase space and found that the oscillation is supplied from a limited region in the phase space that contains the bifurcating orbit. We also show that the period of the oscillation is in good agreement with the period of a contribution from the bifurcating orbit to the semiclassical TPCF obtained by Gutzwiller’s trace formula [J. Math. Phys. 12, 343 (1971)].

scholarly journals When is a dynamical system mean sensitive?

2017 ◽  
Vol 39 (06) ◽  
pp. 1608-1636 ◽  
Author(s):  
FELIPE GARCÍA-RAMOS ◽  
JIE LI ◽  
RUIFENG ZHANG
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
The Other ◽  
Positive Entropy ◽  
Topological Dynamical System ◽  
Other Hand ◽  
Open Question ◽  
Uniquely Ergodic ◽  
Mean Sensitivity ◽  
Transitive System

This article is devoted to studying which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things, we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive. On the other hand, we provide an example of a transitive system which is cofinitely sensitive or Devaney chaotic with positive entropy but fails to be mean sensitive. As applications of our theory and examples, we negatively answer an open question regarding equicontinuity/sensitivity dichotomies raised by Tu, we introduce and present results of locally mean equicontinuous systems and we show that mean sensitivity of the induced hyperspace does not imply that of the phase space.

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