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Lyapunov exponents, dual Lyapunov exponents, and multifractal analysis
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1999It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of one-dimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps.
Fan, Aihua, Jiang, Yunping
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Physical Review A, 1992
The definition of a Lyapunov exponent can be extended to include an imaginary part. This extension requires the definition of a coordinate frame on the tangent space of the differential equation and an extension of the concept of a limit. The definition of extended Lyapunov exponents is based on the eigenvalues of the fundamental matrix.
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The definition of a Lyapunov exponent can be extended to include an imaginary part. This extension requires the definition of a coordinate frame on the tangent space of the differential equation and an extension of the concept of a limit. The definition of extended Lyapunov exponents is based on the eigenvalues of the fundamental matrix.
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Differentiability of Lyapunov Exponents
Journal of Dynamical and Control Systems, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferraiol, Thiago F. +1 more
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Perturbations with nonpositive Lyapunov exponents
Quaestiones Mathematicae, 2022The notion of uniform hyperbolicity is equivalent to various admissibility properties. For example, one such property is expressed in terms of the existence of bounded solutions for any bounded perturbation of the dynamics. Our main objective is to describe a weaker hyperbolicity property for a nonautonomous dynamics with discrete time that
Barreira, Luis, Valls, Claudia
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Physics Letters A, 1987
Abstract A quantal analogue of the maximum Lyapunov exponent αq is defined on the basis of the Q-representation of the density operator. Its usefulness is examined for typical chaotic non-autonomous systems with 2 degrees of freedom. For a homogeneously unstable system this exponent agrees quite well with the classical one, but it is much less than ...
M. Toda, K. Ikeda
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Abstract A quantal analogue of the maximum Lyapunov exponent αq is defined on the basis of the Q-representation of the density operator. Its usefulness is examined for typical chaotic non-autonomous systems with 2 degrees of freedom. For a homogeneously unstable system this exponent agrees quite well with the classical one, but it is much less than ...
M. Toda, K. Ikeda
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2003
Abstract Although there is no universally accepted definition of chaos, most experts would concur that chaos is the aperiodic, long-term behavior of a bounded, deterministic system that exhibits sensitive dependence on initial conditions.
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Abstract Although there is no universally accepted definition of chaos, most experts would concur that chaos is the aperiodic, long-term behavior of a bounded, deterministic system that exhibits sensitive dependence on initial conditions.
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2015
Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in ...
Arkady Pikovsky, Antonio Politi
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Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in ...
Arkady Pikovsky, Antonio Politi
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LYAPUNOV EXPONENTS ON METRIC SPACES
Bulletin of the Australian Mathematical Society, 2017We use the pointwise Lipschitz constant to define an upper Lyapunov exponent for maps on metric spaces different to that given by Kifer [‘Characteristic exponents of dynamical systems in metric spaces’, Ergodic Theory Dynam. Systems3(1) (1983), 119–127].
C. A. MORALES +2 more
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