scholarly journals Spectral transition line for the extended Harper's model in the positive Lyapunov exponent regime

2018 ◽  
Vol 275 (3) ◽  
pp. 712-734 ◽  
Author(s):  
Fan Yang
Keyword(s):  
Lyapunov Exponent ◽  
Positive Lyapunov Exponent ◽  
Transition Line ◽  
Spectral Transition

On maximizing the positive Lyapunov exponent of chaotic oscillators applying DE and PSO

2019 ◽  
Vol 7 (4) ◽  
pp. 1157-1172 ◽  
Author(s):  
Alejandro Silva-Juárez ◽  
Carlos Javier Morales-Pérez ◽  
Luis Gerardo de la Fraga ◽  
Esteban Tlelo-Cuautle ◽  
José de Jesús Rangel-Magdaleno
Keyword(s):  
Lyapunov Exponent ◽  
Positive Lyapunov Exponent ◽  
Chaotic Oscillators

scholarly journals A relation between Lyapunov exponents, Hausdorff dimension and entropy

1981 ◽  
Vol 1 (4) ◽  
pp. 451-459 ◽  
Author(s):  
Anthony Manning
Keyword(s):  
Lyapunov Exponent ◽  
Hausdorff Dimension ◽  
Invariant Measure ◽  
Lyapunov Exponents ◽  
Unstable Manifold ◽  
Positive Lyapunov Exponent ◽  
Axiom A ◽  
Generic Points

AbstractFor an Axiom A diffeomorphism of a surface with an ergodic invariant measure we prove that the entropy is the product of the positive Lyapunov exponent and the Hausdorff dimension of the set of generic points in an unstable manifold.

CHARACTERIZATION OF CHAOTICITY IN THE TRANSIENT CURRENT THROUGH PMMA THIN FILMS

Fractals ◽  
2006 ◽  
Vol 14 (02) ◽  
pp. 125-131 ◽  
Author(s):  
A. HACINLIYAN ◽  
Y. SKARLATOS ◽  
H. A. YILDIRIM ◽  
G. SAHIN
Keyword(s):  
Thin Films ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Power Law ◽  
Chaotic Behavior ◽  
Transient Current ◽  
Positive Lyapunov Exponent ◽  
Aluminum Films ◽  
Thin Aluminum

Chaotic behavior in the transient current through thin Aluminum-PMMA-Aluminum films has been analyzed for times ranging up to 30,000s, in the temperature range 293–363K for applied voltages in the range 10–80V. Time series analysis reveals a positive Lyapunov exponent consistently and reproducibly throughout this range. Power law relaxation as reflected by the autocorrelation function and the positive Lyapunov exponent show parallel behaviors as a function of applied electric field.

Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm

2018 ◽  
Vol 112 ◽  
pp. 36-43 ◽  
Author(s):  
Márcia L.C. Peixoto ◽  
Erivelton G. Nepomuceno ◽  
Samir A.M. Martins ◽  
Márcio J. Lacerda
Keyword(s):  
Lyapunov Exponent ◽  
Least Square ◽  
Positive Lyapunov Exponent ◽  
Recursive Least Square ◽  
Recursive Least Square Algorithm

ALGORITHMS FOR OBTAINING A SADDLE TORUS BETWEEN TWO ATTRACTORS

2013 ◽  
Vol 23 (09) ◽  
pp. 1330032 ◽  
Author(s):  
KYOHEI KAMIYAMA ◽  
MOTOMASA KOMURO ◽  
TETSURO ENDO
Keyword(s):  
Lyapunov Exponent ◽  
Periodic Orbit ◽  
Pattern Matching ◽  
The Other ◽  
Lyapunov Spectrum ◽  
Positive Lyapunov Exponent ◽  
Template Method ◽  
Bisection Method ◽  
Basin Boundary ◽  
Wave Solutions

We develop two algorithms for obtaining an index 1 saddle torus between two attractors of which basin boundary is smooth by using the bisection method. In the first algorithm, which we name "overall template method", we make a template approximating a whole attractor and use it for pattern matching. The attractor can be a periodic orbit, a torus and even a chaos. In the second algorithm, which we name "partial template method", we make a template approximating only a part of an attractor. In this algorithm, the attractor is restricted to a periodic orbit and a two-torus, but calculation time is much smaller than that of the overall template method. We demonstrate these two algorithms for two solutions, observed in a ring of six-coupled bistable oscillators. One is a saddle torus in the basin boundary of the two switching solutions, and the other is of the two quasi-periodic propagating wave solutions. We calculate the Lyapunov spectrum of the obtained saddle torus, and confirm one positive Lyapunov exponent.

scholarly journals The entropy of C2 surface diffeomorphisms in terms of Hausdorff dimension and a Lyapunov exponent

1985 ◽  
Vol 5 (2) ◽  
pp. 273-283 ◽  
Author(s):  
Leonardo Mendoza
Keyword(s):  
Lyapunov Exponent ◽  
Hausdorff Dimension ◽  
Ergodic Measure ◽  
Positive Lyapunov Exponent ◽  
Stable Manifolds ◽  
Surface Diffeomorphisms ◽  
The Family ◽  
Surface Diffeomorphism

AbstractIn this paper we prove that if the entropy of an ergodic measure preserved by a C2 surface diffeomorphism is positive then it is equal to the product of the Hausdorff dimension of the quotient measure defined by the family of stable manifolds and the positive Lyapunov exponent.

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