The Metric Entropy of Diffeomorphisms: Part I: Characterization of Measures Satisfying Pesin's Entropy Formula

1985 ◽  
Vol 122 (3) ◽  
pp. 509 ◽  
Author(s):  
F. Ledrappier ◽  
L.-S. Young
Keyword(s):  
Metric Entropy ◽  
Entropy Formula ◽  
Pesin’S Entropy Formula

Ergodic theory for axiom A endomorphisms

1995 ◽  
Vol 15 (1) ◽  
pp. 161-174 ◽  
Author(s):  
Min Qian ◽  
Zhusheng Zhang
Keyword(s):  
Ergodic Theorem ◽  
Ergodic Theory ◽  
Axiom A ◽  
Entropy Formula ◽  
Pesin’S Entropy Formula

AbstractIn this paper the Pesin's entropy formula and ‘large ergodic theorem’ are constructed for Axiom A endomorphisms.

scholarly journals CHARACTERIZATION OF LASER PROPAGATION THROUGH TURBULENT MEDIA BY QUANTIFIERS BASED ON THE WAVELET TRANSFORM

Fractals ◽  
2004 ◽  
Vol 12 (02) ◽  
pp. 223-233 ◽  
Author(s):  
LUCIANO ZUNINO ◽  
DARÍO G. PÉREZ ◽  
MARIO GARAVAGLIA ◽  
OSVALDO A. ROSSO
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hurst Exponent ◽  
Wavelet Theory ◽  
Complementary Information ◽  
Laser Propagation ◽  
Entropy Formula ◽  
Center Position ◽  
The Mean

The propagation of a laser beam through turbulent media is modeled as a fractional Brownian motion (fBm). Time series corresponding to the center position of the laser spot (coordinates x and y) after traveling across air in turbulent motion, with different strength, are analyzed by the wavelet theory. Two quantifiers are calculated, the Hurst exponent, H, and the mean Normalized Total Wavelet Entropy, [Formula: see text]. It is verified that both quantifiers give complementary information about the turbulence.

Stretching Generic Pesin’s Entropy Formula

2018 ◽  
Vol 173 (5) ◽  
pp. 1523-1546
Author(s):  
Mário Bessa ◽  
César M. Silva ◽  
Helder Vilarinho
Keyword(s):  
Entropy Formula ◽  
Pesin’S Entropy Formula

scholarly journals Pesin’s entropy formula for endomorphisms

1998 ◽  
Vol 150 ◽  
pp. 197-209 ◽  
Author(s):  
Pei-Dong Liu
Keyword(s):  
Compact Manifold ◽  
Smooth Measure ◽  
Entropy Formula ◽  
Pesin’S Entropy Formula

Abstract.In this paper we prove Pesin’s entropy formula for general C2 (or C1+α) (non-invertible) endomorphisms of a compact manifold preserving a smooth measure.

scholarly journals The Pesin entropy formula for diffeomorphisms with dominated splitting

2014 ◽  
Vol 35 (3) ◽  
pp. 737-761 ◽  
Author(s):  
ELEONORA CATSIGERAS ◽  
MARCELO CERMINARA ◽  
HEBER ENRICH
Keyword(s):  
Lyapunov Exponents ◽  
Invariant Measures ◽  
Metric Entropy ◽  
Dominated Splitting ◽  
Dirac Delta ◽  
Asymptotic Statistics ◽  
Entropy Formula ◽  
Almost All

AbstractFor any$C^1$diffeomorphism with dominated splitting, we consider a non-empty set of invariant measures that describes the asymptotic statistics of Lebesgue-almost all orbits. They are the limits of convergent subsequences of averages of the Dirac delta measures supported on those orbits. We prove that the metric entropy of each of these measures is bounded from below by the sum of the Lyapunov exponents on the dominating sub-bundle. As a consequence, if those exponents are non-negative, and if the exponents on the dominated sub-bundle are non-positive, those measures satisfy the Pesin entropy formula.

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