相关论文: Ruelle transfer operators for contact Anosov flows…
For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame flow with respect to the normalized volume. More generally this result extends to…
We analyze the properties of the edge states of the one-dimensional Kitaev model with long-range anisotropic pairing and tunneling. Tunneling and pairing are assumed to decay algebraically with exponents $\alpha$ and $\beta$, respectively,…
The existence of measure preserving invertible transformations $T$ with simple spectrum is established possessing the following rate of correlation decay $(f(T^k x), f(x)) = O(|k|^{-1/2+{\epsilon}})$ for a dense family of functions $f$ and…
We show that for smooth contact Anosov flows in dimension 3, the resonant states associated to the first band of Ruelle resonances are distributions that are killed by the unstable derivative.
We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, $O(N)$-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin…
We prove that an Anosov action of $\mathbb{R}^k$ over a compact manifold $M$ transitive on regular sub-cones satisfies the dichotomy: each stable and unstable leaf is dense or the Anosov action is topologically conjugated to a suspension of…
We introduce a weak transversality condition for piecewise C^{1+\alpha} and piecewise hyperbolic maps which admit a C^{1+\alpha} stable distribution. We show good bounds on the essential spectral radius of the associated transfer operators…
The two-point correlation function of a Potts model on a graph $G$ may be expressed in terms of the flow polynomials of `Poissonian' random graphs derived from $G$ by replacing each edge by a Poisson-distributed number of copies of itself.…
Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…
The two-dimensional random-bond Ising model is numerically studied on long strips by transfer-matrix methods. It is shown that the rate of decay of correlations at criticality, as derived from averages of the two largest Lyapunov exponents…
We show that any weak solution of the Gabitov-Turitsyn equation describing dispersion managed solitons together with its Fourier transform decay exponentially. This strong regularity result extends a recent result of Erdogan, Hundertmark…
Suppose the auto-correlations of real-valued, centered Gaussian process $Z(\cdot)$ are non-negative and decay as $\rho(|s-t|)$ for some $\rho(\cdot)$ regularly varying at infinity of order $-\alpha \in [-1,0)$. With $I_\rho(t)=\int_0^t…
We introduce numerical invariants of contact forms in dimension three and use asymptotic cycles to estimate them. As a consequence, we prove a version for Anosov Reeb flows of results due to Hutchings and Weiler on mean actions of periodic…
In this note, we establish an original result for the thermodynamic formalism in the context of expanding circle transformations with an indifferent fixed point. For an observable whose continuity modulus is linked to the dynamics near such…
We study hyperbolic attractors of some dynamical systems with apriori given countable Markov partitions. Assuming that contraction is stronger than expansion we construct new Markov rectangles such that their crossections by unstable…
Several results in previous works, strongly depend on the exponential tail of the linkages' distribution in our adhesive models. The purpose of this paper is to weaken this hypothesis and to allow more fat tails for large ages. From the…
We establish expansion of every order for the correlation function of sufficiently regular observables of $\mathbb Z^d$ extensions of some hyperbolic flows. Our examples include the $\mathbb Z^2$ periodic Lorentz gas and geodesic flows on…
We evaluate radiative decays of $\rho$ and $\omega$ going to two neutral mesons, $\pi^{0} \pi^{0}$ and $\pi^{0} \eta$. We use the sequential vector decay mechanisms in addition to chiral loops and $\rho$-$\omega$ mixing. The chiral loops…
In a previous paper with C. Bonatti ([5]), we have defined a general procedure to build new examples of Anosov flows in dimension 3. The procedure consists in gluing together some building blocks, called hyperbolic plugs, along their…
We prove a generalization of a so called "invariance principle" for partially hyperbolic diffeomorphisms: if an invariant probability measure has all its center Lyapunov exponents equal to zero then the measure admits a center…