# Stability of mixing and rapid mixing for hyperbolic flows | Annals of Mathematics

Abstract We obtain general results on the stability of mixing and rapid mixing (superpolynomial decay of correlations) for hyperbolic flows. Amongst Cr Axiom A flows, r≥2, we show that there is a C2-open, Cr-dense set of flows for which each nontrivial hyperbolic basic set is rapid mixing. This is the first general result on the stability of rapid mixing (or even mixing) for Axiom A flows that holds in a Cr, as opposed to Hölder, topology.

KEYWORDS

SHARE & LIKE

COMMENTS

ABOUT THE AUTHOR

### 数学年刊（Annals of Mathematics）

0 Following 0 Fans 0 Projects 674 Articles

SIMILAR ARTICLES

Abstract For any nondegenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a correspondin

Read More

Abstract For a large class of nonlinear Schrödinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity, we

Read More

Abstract Let L2,p(ℝ2) be the Sobolev space of real-valued functions on the plane whose Hessian belongs to Lp. For any finite subset E⊂ℝ2 and p>2, let

Read More

Abstract We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra LG completely

Read More

Abstract We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We

Read More

Abstract This paper has two main results. Firstly, we complete the parametrisation of all p-blocks of finite quasi-simple groups by finding the so-cal

Read More

Abstract We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for ge

Read More

Abstract We prove that isoparametric hypersurfaces with (g,m)=(6,2) are homogeneous, which answers Dorfmeister-Neher’s conjecture affirmatively and so

Read More

Abstract We prove the periodicity conjecture for pairs of Dynkin diagrams using Fomin-Zelevinsky’s cluster algebras and their (additive) categorificat

Read More

Abstract If F(x,y)∈ℤ[x,y] is an irreducible binary form of degree k≥3, then a theorem of Darmon and Granville implies that the generalized superellipt

Read More