scholarly journals Conformally Symplectic Dynamics and Symmetry of the Lyapunov Spectrum

1998 ◽  
Vol 194 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Maciej P. Wojtkowski ◽  
Carlangelo Liverani
Keyword(s):  
Lyapunov Spectrum ◽  
Symplectic Dynamics

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.

CHAOS AND TWO-TORI IN A NEW FAMILY OF 4-CNNS

2007 ◽  
Vol 17 (03) ◽  
pp. 953-963 ◽  
Author(s):  
XIAO-SONG YANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Cellular Neural Networks ◽  
Lyapunov Spectrum ◽  
Regular Array ◽  
Poincaré Maps ◽  
One Dimensional ◽  
Poincare Maps ◽  
New Family

In this paper we demonstrate chaos, two-tori and limit cycles in a new family of Cellular Neural Networks which is a one-dimensional regular array of four cells. The Lyapunov spectrum is calculated in a range of parameters, the bifurcation plots are presented as well. Furthermore, we confirm the nature of limit cycle, chaos and two-tori by studying Poincaré maps.

scholarly journals Simple Lyapunov spectrum for certain linear cocycles over partially hyperbolic maps

Nonlinearity ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 238-284
Author(s):  
Mauricio Poletti ◽  
Marcelo Viana
Keyword(s):  
Lyapunov Spectrum ◽  
Partially Hyperbolic

scholarly journals Symplectic dynamics and the 3-sphere

2019 ◽  
Vol 235 (1) ◽  
pp. 245-254
Author(s):  
Marc Kegel ◽  
Jay Schneider ◽  
Kai Zehmisch
Keyword(s):  
Symplectic Dynamics

scholarly journals The Lyapunov spectrum of some parabolic systems

2009 ◽  
Vol 29 (3) ◽  
pp. 919-940 ◽  
Author(s):  
KATRIN GELFERT ◽  
MICHAŁ RAMS
Keyword(s):  
Lyapunov Exponent ◽  
Hausdorff Dimension ◽  
Lyapunov Exponents ◽  
Topological Entropy ◽  
Level Set ◽  
Level Sets ◽  
Parabolic Systems ◽  
Lyapunov Spectrum ◽  
Interval Maps ◽  
Set Of Points

AbstractWe study the Hausdorff dimension for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given lower and upper Lyapunov exponents and, in particular, with zero lower Lyapunov exponent. We prove that the level set of points with zero exponent has full Hausdorff dimension, but carries no topological entropy.

Towards the Full Lyapunov Spectrum of Elementary Cellular Automata

2011 ◽  
Author(s):  
J. M. Baetens ◽  
B. De Baets ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Cellular Automata ◽  
Lyapunov Spectrum ◽  
Elementary Cellular Automata

scholarly journals On the Lyapunov spectrum for rational maps

2010 ◽  
Vol 348 (4) ◽  
pp. 965-1004 ◽  
Author(s):  
Katrin Gelfert ◽  
Feliks Przytycki ◽  
Michał Rams
Keyword(s):  
Lyapunov Spectrum ◽  
Rational Maps
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