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Positive Lyapunov exponents for symplectic cocycles
, 2014
"... In the present paper we give a positive answer to a question posed by Viana in [22] on the existence of positive Lyapunov exponents for symplectic cocycles. Actually, we prove that for an open and dense set of Hölder symplectic cocycles over a nonuniformly hyperbolic diffeomorphism there are non ..."
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In the present paper we give a positive answer to a question posed by Viana in [22] on the existence of positive Lyapunov exponents for symplectic cocycles. Actually, we prove that for an open and dense set of Hölder symplectic cocycles over a nonuniformly hyperbolic diffeomorphism there are non
POSITIVE LYAPUNOV EXPONENT BY A RANDOM PERTURBATION
"... Abstract. We study the effect of a random perturbation on a oneparameter family of dynamical systems whose behavior in the absence of perturbation is ill understood. We provide conditions under which the perturbed system is ergodic and admits a positive Lyapunov exponent, with an explicit lower bou ..."
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Abstract. We study the effect of a random perturbation on a oneparameter family of dynamical systems whose behavior in the absence of perturbation is ill understood. We provide conditions under which the perturbed system is ergodic and admits a positive Lyapunov exponent, with an explicit lower
Positive Lyapunov exponents for Hamiltonian linear differential systems
, 2014
"... Abstract. In the present paper we give a positive answer to some questions posed in [39] on the existence of positive Lyapunov exponents for symplectic and Hamiltonian cocycles. Actually, we prove that for an open and dense set of Hölder symplectic cocycles over a nonuniformly hyperbolic diffeomor ..."
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Abstract. In the present paper we give a positive answer to some questions posed in [39] on the existence of positive Lyapunov exponents for symplectic and Hamiltonian cocycles. Actually, we prove that for an open and dense set of Hölder symplectic cocycles over a nonuniformly hyperbolic
Printed in Great Britain Positive Lyapunov exponents for a
, 1990
"... Abstract Let T be an aperiodic automorphism of a standard probability space (X, m) We prove, that the set hm n'log>i(r' n*oo I 1 x) A(Tx)A(x)\\>0,, is dense in L°°(X, SL(2, R)) ..."
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Abstract Let T be an aperiodic automorphism of a standard probability space (X, m) We prove, that the set hm n'log>i(r' n*oo I 1 x) A(Tx)A(x)\\>0,, is dense in L°°(X, SL(2, R))
UNIFORM HYPERBOLICITY FOR RANDOM MAPS WITH POSITIVE LYAPUNOV EXPONENTS
, 2007
"... Abstract. We consider some general classes of random dynamical systems and show that a priori very weak nonuniform hyperbolicity conditions actually imply uniform hyperbolicity. ..."
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Abstract. We consider some general classes of random dynamical systems and show that a priori very weak nonuniform hyperbolicity conditions actually imply uniform hyperbolicity.
HYPERBOLICITY ESTIMATES FOR RANDOM MAPS WITH POSITIVE LYAPUNOV EXPONENTS
, 2006
"... In this paper we consider smooth random dynamical systems F over an abstract dynamical systems (Ω, F, P, θ), where (Ω, F, P) is a complete probability space and θ: Ω → Ω is a P preserving ergodic invertible transformation. More specifically, we have a skewproduct ..."
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In this paper we consider smooth random dynamical systems F over an abstract dynamical systems (Ω, F, P, θ), where (Ω, F, P) is a complete probability space and θ: Ω → Ω is a P preserving ergodic invertible transformation. More specifically, we have a skewproduct
characterization of transition to chaos with multiple positive Lyapunov exponents by unstable periodic orbits
, 2000
"... We investigate how the transition to chaos with multiple positive Lyapunov exponents can be characterized by the set of infinite number of unstable periodic orbits embedded in the chaotic invariant set. We argue and provide numerical confirmation that the transition is generally accompanied by a non ..."
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We investigate how the transition to chaos with multiple positive Lyapunov exponents can be characterized by the set of infinite number of unstable periodic orbits embedded in the chaotic invariant set. We argue and provide numerical confirmation that the transition is generally accompanied by a
Measures with positive Lyapunov exponent and conformal measures in rational dynamics
"... Abstract. Ergodic properties of rational maps are studied, generalising the work of F. Ledrappier. A new construction allows for simpler proofs of stronger results. Very general conformal measures are considered. Equivalent conditions are given for an ergodic invariant probability measure with posit ..."
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Cited by 10 (2 self)
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with positive Lyapunov exponent to be absolutely continuous with respect to a general conformal measure. If they hold, we can construct an induced expanding Markov map with integrable return time which generates the invariant measure. 1.
Limitperiodic Schrödinger operators in the regime of positive Lyapunov exponents
, 2009
"... We investigate the spectral properties of the discrete onedimensional Schrödinger operators whose potentials are generated by continuous sampling along the orbits of a minimal translation of a Cantor group. We show that for given Cantor group and minimal translation, there is a dense set of conti ..."
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Cited by 9 (7 self)
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of continuous sampling functions such that the spectrum of the associated operators has zero Hausdorff dimension and all spectral measures are purely singular continuous. The associated Lyapunov exponent is a continuous strictly positive function of the energy. It is possible to include a coupling constant
Results 1  10
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227,012