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
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova

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.


1999 ◽  
Vol 258 (1) ◽  
pp. 25-30 ◽  
Author(s):  
Martin J. Bünner ◽  
R. Hegger

2000 ◽  
Vol 138 ◽  
pp. 592-593
Author(s):  
Tsuneyasu Okabe ◽  
Hiroaki Yamada

Author(s):  
Nayyer Iqbal ◽  
Shahid Ahmad ◽  
Muhammad Hussain
Keyword(s):  

2006 ◽  
Vol 24 (1) ◽  
pp. 9-14 ◽  
Author(s):  
M. KANAPATHIPILLAI

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.


2020 ◽  
pp. 1-38
Author(s):  
TIANYU WANG

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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