Titlebook: Lyapunov Exponents; Luís Barreira Book 2017 Springer International Publishing AG 2017 regularity.hyperbolicity.ergodic theory.multifractal

Cryptic

Linear Differential Equationsrity can be characterized in terms of exponential growth rates of volumes and we establish various important properties of regular equations. Finally, we consider the stronger notion of regularity for a two-sided coefficient matrix.

急急忙忙

Lyapunov Functions and Conesapunov exponent in terms of invariant cone families. We note that the theory is essentially different in the cases of a cocycle and of a single sequence of matrices, mainly because in the latter case one cannot use the powerful tools of ergodic theory.

TATE

Entropy Spectrum the Lyapunov exponent takes uncountably many values, with each of them attained in a dense set of positive topological entropy. We also briefly describe a corresponding entropy spectrum for the Lyapunov exponent on a conformal hyperbolic set.

galley

Lyapunov Sequencesversion for a single trajectory of corresponding results for cocycles over a measure-preserving transformation. Unsurprisingly, the powerful tools of ergodic theory allow that the corresponding hypotheses in the notion of a Lyapunov function are weaker in the context of ergodic theory.

Palpitation

NAVEN

Gum-Disease

Lyapunov Exponents and Regularityential equations. These two classes of Lyapunov exponents are the main objects of study in the book. Finally, we introduce the Perron coefficient and we use it to give an alternative characterization of Lyapunov regularity, in terms of the values of the dual Lyapunov exponents used to define the Grobman coefficient.

美色花钱

Adjourn

巫婆

Cocycles and Lyapunov Exponentsderivative cocycle of a differentiable map. Namely, we introduce numbers that play the role of the values of the Lyapunov exponent for maps that are not necessarily differentiable. These turn out to coincide on a repeller for a differentiable map, for almost every point with respect to an invariant measure.