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COVARIANT LYAPUNOV EXPONENTS FOR THE MIXMASTER
, 2004
"... The dynamics of the Mixmaster Universe is analized in a covariant picture via Misner– Chitrelike variables for an ADM Hamiltonian approach. The system outcomes as isomorphic to a billiard on the Lobachevsky plane and Lyapunov exponents are calculated explicitly. 1. ..."
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The dynamics of the Mixmaster Universe is analized in a covariant picture via Misner– Chitrelike variables for an ADM Hamiltonian approach. The system outcomes as isomorphic to a billiard on the Lobachevsky plane and Lyapunov exponents are calculated explicitly. 1.
Transformation invariance of Lyapunov exponents
 CHAOS, SOLITONS AND FRACTALS
, 2001
"... Lyapunov exponents represent important quantities to characterize the properties of dynamical systems. We show that the Lyapunov exponents of two different dynamical systems that can be converted to each other by a transformation of variables are identical. Moreover, we derive sufficient conditions ..."
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Lyapunov exponents represent important quantities to characterize the properties of dynamical systems. We show that the Lyapunov exponents of two different dynamical systems that can be converted to each other by a transformation of variables are identical. Moreover, we derive sufficient conditions
Lyapunov Exponents of Symmetric Attractors
, 2006
"... The Lyapunov exponents of symmetric attractors can be forced to be multiple by \instantaneous symmetries " which x the attractor pointwise. In this paper, we show that \symmetries on average " which x the attractor as a set may lead to further multiplicities. This work is motivated by, an ..."
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The Lyapunov exponents of symmetric attractors can be forced to be multiple by \instantaneous symmetries " which x the attractor pointwise. In this paper, we show that \symmetries on average " which x the attractor as a set may lead to further multiplicities. This work is motivated by
FORMULAS FOR LYAPUNOV EXPONENTS
"... Abstract. We derive a series summation formula for the average logarithm norm of the action of a matrix on the projective space. This formula is shown to be useful to evaluate some Lyapunov exponents of random SLmatrix cocycles, which include a special class for which H. Furstenberg had provided an ..."
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Abstract. We derive a series summation formula for the average logarithm norm of the action of a matrix on the projective space. This formula is shown to be useful to evaluate some Lyapunov exponents of random SLmatrix cocycles, which include a special class for which H. Furstenberg had provided
Cellular automata and Lyapunov exponents
 Nonlinearity
"... The first definition of Lyapunov exponents (depending on a probability measure) for a onedimensional cellular automaton were introduced by Shereshevsky in 1991. The existence of an almost everywhere constant value for each of the two exponents (left and right), requires particular conditions for th ..."
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Cited by 7 (2 self)
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The first definition of Lyapunov exponents (depending on a probability measure) for a onedimensional cellular automaton were introduced by Shereshevsky in 1991. The existence of an almost everywhere constant value for each of the two exponents (left and right), requires particular conditions
GENERICITY OF ZERO LYAPUNOV EXPONENTS
, 2002
"... Abstract. We show that, for any compact surface, there is a residual (dense Gδ) set of C 1 area preserving diffeomorphisms which either are Anosov or have zero Lyapunov exponents a.e. This result was announced by R. Mañé, but no proof was available. We also show that for any fixed ergodic dynamical ..."
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Abstract. We show that, for any compact surface, there is a residual (dense Gδ) set of C 1 area preserving diffeomorphisms which either are Anosov or have zero Lyapunov exponents a.e. This result was announced by R. Mañé, but no proof was available. We also show that for any fixed ergodic dynamical
Lyapunov Exponents for the Stadium Billiard
, 1995
"... Contents 1 Introduction 2 1.1 The Bunimovich Stadium : : : : : : : : : : : : : : : : : : : : : : 2 2 Lyapunov Exponent 2 2.1 Definition : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.2 For the Stadium Billiard : : : : : : : : : : : : : : : : : : : : : : : 3 2.2.1 Theory : : : ..."
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Contents 1 Introduction 2 1.1 The Bunimovich Stadium : : : : : : : : : : : : : : : : : : : : : : 2 2 Lyapunov Exponent 2 2.1 Definition : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.2 For the Stadium Billiard : : : : : : : : : : : : : : : : : : : : : : : 3 2.2.1 Theory
Generic properties of Lyapunov exponents
 Random and Computational Dynamics
, 1994
"... We prove that the Lyapunov exponents repeated according to their multiplicities are Baire functions of the first class, and the dimensions of the Oseledets subspaces are Baire functions of the second class. As a consequence, the repeated Lyapunov exponents are generically continuous. 1 Introduction ..."
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We prove that the Lyapunov exponents repeated according to their multiplicities are Baire functions of the first class, and the dimensions of the Oseledets subspaces are Baire functions of the second class. As a consequence, the repeated Lyapunov exponents are generically continuous. 1 Introduction
Entropy potential and Lyapunov exponents
"... According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function, the entropy potential. The validity and the consequences of this hypothesis are explored in detail. The numerical investigation of a conti ..."
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According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function, the entropy potential. The validity and the consequences of this hypothesis are explored in detail. The numerical investigation of a
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