On Contact Anosov Flows

Exponential decay of correlations for \Co^{(4)} Contact Anosov flows is established. This implies, in particular, exponential decay of correlations for all smooth geodesic flows in strictly negative curvature

Fredholm determinants, Anosov maps and Ruelle resonances

I show that the dynamical determinant, associated to an Anosov diffeomorphism, is the Fredholm determinant of the corresponding Ruelle-Perron-Frobenius transfer operator acting on appropriate Banach spaces. As a consequence it follows, for example, that the zeroes of the dynamical determinant describe the eigenvalues of the transfer operator and the Ruelle resonances and that, for \Co^\infty Anosov diffeomorphisms, the dynamical determinant is an entire function

Climate change and individual behavior : considerations for policy

Climate change is anthropogenic - the product of billions of acts of daily consumption. That solutions need to be anthropogenic too is well accepted. Yet, suggested solutions are normally cast in the realms of finance and technology, often neglecting the primal root of the problem: individual behavior. An emerging body of social-psychology scholarship has examined the barriers and drivers of individual behavior in relation to both adaptation and mitigation. This paper reviews some of its conclusions, and suggests policy areas that should be considered in devising appropriate interventions.Environmental Economics&Policies,Climate Change,Transport and Environment,Energy Production and Transportation,Environment and Energy Efficiency

Banach spaces adapted to Anosov systems

We study the spectral properties of the Ruelle-Perron-Frobenius operator associated to an Anosov map on classes of functions with high smoothness. To this end we construct anisotropic Banach spaces of distributions on which the transfer operator has a small essential spectrum. In the C^\infty case, the essential spectral radius is arbitrarily small, which yields a description of the correlations with arbitrary precision. Moreover, we obtain sharp spectral stability results for deterministic and random perturbations. In particular, we obtain differentiability results for spectral data (which imply differentiability of the SRB measure, the variance for the CLT, the rates of decay for smooth observable, etc.).Comment: 26 page

Toward the Fourier law for a weakly interacting anharmonic crystal

For a system of weakly interacting anharmonic oscillators, perturbed by an energy preserving stochastic dynamics, we prove an autonomous (stochastic) evolution for the energies at large time scale (with respect to the coupling parameter). It turn out that this macroscopic evolution is given by the so called conservative (non-gradient) Ginzburg-Landau system of stochastic differential equations. The proof exploits hypocoercivity and hypoellipticity properties of the uncoupled dynamics

Convergence to equilibrium for intermittent symplectic maps

We investigate a class of area preserving non-uniformly hyperbolic maps of the two torus. First we establish some results on the regularity of the invariant foliations, then we use this knowledge to estimate the rate of mixing.Comment: LaTeX, 23 page

Map Lattices coupled by collisions

We introduce a new coupled map lattice model in which the weak interaction takes place via rare "collisions". By "collision" we mean a strong (possibly discontinuous) change in the system. For such models we prove uniqueness of the SRB measure and exponential space-time decay of correlations