Existence of C^{K}-invariant foliations for Lorenz type maps

Abstract

In this paper under similar conditions to that Shaskov and Shil'nikov [1994] we show that a C^{k+1} Lorenz-type map T has a C^{k} foliation which is invariant under T. This allows us to associate T to a C^{k} one-dimensional transformation.

33 pages and 3 figures

References in corpus (3)

• Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps
• Robust exponential decay of correlations for singular-flows
• On the Hyperbolicity of Lorenz Renormalization

Cited by in corpus (1)

• Finitely many physical measures for sectional-hyperbolic attracting sets and statistical stability