Lyapunov exponent for Lipschitz maps

On Lipschitz Continuity of the Top Lyapunov Exponent of Linear Parameter Varying and Linear Switching Systems

We study families of time-varying linear systems, where time-variations have to satisfy restrictions on the dwell time, that is, on the minimum distance between discontinuities, as well as on the derivative in between discontinuities. For this class of systems we study continuity properties of the growth rate as a function of the systems’ data. It is shown by example, that a straightforward top...

Return Time Statistics for Invariant Measures for Interval Maps with Positive Lyapunov Exponent

We prove that multimodal maps with an absolutely continuous invariant measure have exponential return time statistics around a.e. point. We also show a ‘polynomial Gibbs property’ for these systems, and that the convergence to the entropy in the Ornstein-Weiss formula has normal fluctuations. These results are also proved for equilibrium states of some Hölder potentials.

lipschitz groups and lipschitz maps

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

Lyapunov Exponent for Products of Random Matrices

Maximal Lyapunov exponent at crises.

We study the variation of Lyapunov exponents of simple dynamical systems near attractor-widening and attractor-merging crises. The largest Lyapunov exponent has universal behaviour, showing abrupt variation as a function of the control parameter as the system passes through the crisis point, either in the value itself, in the case of the attractor-widening crisis, or in the slope, for attractor...