Exponential decay of correlations for piecewise cone hyperbolic contact flows

TY - JOUR

T1 - Exponential decay of correlations for piecewise cone hyperbolic contact flows

AU - Baladi, Viviane

AU - Liverani, Carlangelo

PY - 2012/9

Y1 - 2012/9

N2 - We prove exponential decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time exponential decay of correlations is proved for continuous-time dynamics with singularities on a manifold. Our proof combines the second author's version (Liverani in Ann Math 159:1275-1312, 2004) of Dolgopyat's estimates for contact flows and the first author's work with Gouëzel (J Mod Dyn 4:91-137, 2010) on piecewise hyperbolic discrete-time dynamics.

AB - We prove exponential decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time exponential decay of correlations is proved for continuous-time dynamics with singularities on a manifold. Our proof combines the second author's version (Liverani in Ann Math 159:1275-1312, 2004) of Dolgopyat's estimates for contact flows and the first author's work with Gouëzel (J Mod Dyn 4:91-137, 2010) on piecewise hyperbolic discrete-time dynamics.

U2 - 10.1007/s00220-012-1538-4

DO - 10.1007/s00220-012-1538-4

M3 - Journal article

SN - 0010-3616

VL - 314

SP - 689

EP - 773

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

ER -