Area expanding C^{1+α} Suspension Semiflows

Abstract

We study a large class of suspension semiflows which contains the Lorenz semiflows. This is a class with low regularity (merely C^{1+α}) and where the return map is discontinuous and the return time is unbounded. We establish the functional analytic framework which is typically employed to study rates of mixing. The Laplace transform of the correlation function is shown to admit a meromorphic extension to a strip about he imaginary axis. As part of this argument we give a new result concerning the quasi-compactness of weighted transfer operators for piecewise C^{1+α} expanding interval maps.

References in corpus (3)

• Exponential decay of correlations for piecewise cone hyperbolic contact flows
• Robust exponential decay of correlations for singular-flows
• Lorenz like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence

Cited by in corpus (7)

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• Parabolic Flows Renormalized by Partially Hyperbolic Maps
• Stochastic stability of the classical Lorenz flow under impulsive type forcing
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• Stretched-exponential mixing for ${\mathcal{C}}^{1+\alpha }$ skew products with discontinuities
• Stochastic and statistical stability of the classical Lorenz flow under perturbations modeling anthropogenic type forcing
• Exponential mixing for singular skew-products