Typical symplectic locally constant cocycles over certain shifts of countable type have simple Lyapunov spectra

2016 ◽  
Vol 73 (3) ◽  
pp. 171-176 ◽  
Author(s):  
Michel Cambrainha ◽  
Carlos Matheus
Keyword(s):  
Countable Type ◽  
Lyapunov Spectra

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

Estimation of Lyapunov spectra from space–time data

1999 ◽  
Vol 258 (1) ◽  
pp. 25-30 ◽  
Author(s):  
Martin J. Bünner ◽  
R. Hegger
Keyword(s):  
Space Time ◽  
Time Data ◽  
Lyapunov Spectra

scholarly journals Lyapunov Spectra of Correlated Random Matrices

2000 ◽  
Vol 138 ◽  
pp. 592-593
Author(s):  
Tsuneyasu Okabe ◽  
Hiroaki Yamada
Keyword(s):  
Random Matrices ◽  
Lyapunov Spectra

scholarly journals LYAPUNOV SPECTRA FOR KAPITZA OSCILLATOR

2012 ◽  
Vol 17 (1) ◽  
Author(s):  
Nayyer Iqbal ◽  
Shahid Ahmad ◽  
Muhammad Hussain
Keyword(s):  
Lyapunov Spectra

scholarly journals Nonlinear absorption of ultra short laser pulses by clusters

2006 ◽  
Vol 24 (1) ◽  
pp. 9-14 ◽  
Author(s):  
M. KANAPATHIPILLAI
Keyword(s):  
Initial Phase ◽  
Nonlinear Oscillator ◽  
Chaotic Behavior ◽  
Nonlinear Resonance ◽  
Laser Pulses ◽  
Cluster Interaction ◽  
Lyapunov Spectra ◽  
Short Laser Pulses ◽  
Established Fact ◽  
Eigen Frequencies

Very good absorption of ultra short laser pulses by clusters is a well established fact. Efficient collisional absorption occurs only in the initial phase of the pulse. However, experiments and numerical simulations show that even after collisional absorption becomes inefficient subsequent to heating of the electrons, strong absorption continues. There have been a few attempts to model this phenomenon in terms of driven “linear” oscillator models with time dependent eigen-frequencies. Here we propose a nonlinear oscillator model and show that nonlinear resonance is the leading mechanism responsible for the collisionless absorption. Further it is demonstrated, on the basis of Lyapunov spectra, that laser-cluster interaction, under certain conditions, exhibits chaotic behavior.

scholarly journals Unique equilibrium states, large deviations and Lyapunov spectra for the Katok map

2020 ◽  
pp. 1-38
Author(s):  
TIANYU WANG
Keyword(s):  
Equilibrium State ◽  
Level Sets ◽  
Additional Condition ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Thermodynamic Formalism ◽  
Hölder Continuous ◽  
Lyapunov Spectra ◽  
Continuous Potential ◽  
Level 2

We study the thermodynamic formalism of a $C^{\infty }$ non-uniformly hyperbolic diffeomorphism on the 2-torus, known as the Katok map. We prove for a Hölder continuous potential with one additional condition, or geometric $t$ -potential $\unicode[STIX]{x1D711}_{t}$ with $t<1$ , the equilibrium state exists and is unique. We derive the level-2 large deviation principle for the equilibrium state of $\unicode[STIX]{x1D711}_{t}$ . We study the multifractal spectra of the Katok map for the entropy and dimension of level sets of Lyapunov exponents.

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