We study the behaviour of a Hilbert geometry when going to infinity along a geodesic line. We prove that all the information is contained in the shape of the boundary at the endpoint of this geodesic line and have to introduce a regularity property of convex functions to make this link precise. The point of view is a dynamical one and the main interest of this article is in Lyapunov exponents o...

The Lyapunov exponents of symmetric attractors can be forced to be multiple by “instantaneous symmetries” which fix the attractor pointwise. In this paper, we show that “symmetries on average” which fix the attractor as a set may lead to further multiplicities. This work is motivated by, and provides an explanation for, numerical computations by Aston & Laing of Lyapunov exponents for the compl...

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 system over a compact space, there is a residual set of continuous SL(2, R)-cocycles which either are unifo...

the threshold of weak and strong synchronization in a coupled chaotic gaussian map isdemonstrated by using the pyragas’ terminology. however, vieira and lichtenberg have shown that thepyragas’ criteria for weak and strong synchronization cannot be used for all chaotic systems. in this articlewe demonstrated some interesting synchronization behavior of two coupled chaotic systems with some zeroa...

Primary audience. Ph.D. students and advanced M.S. students interested in stochastic processes. General Course Description. A basic course which introduces the topic of stochastic partial di¤erential equations (SPDEs) via some simple examples that are amenable to detailed calculations, focusing mainly on parabolic equations. The prerequisite for the course being only a graduate course in probab...

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 continuous-time model provides a further confirmation to the existence of the entropy potential. Furthe...