37 research outputs found
Thermodynamic formalism for contracting Lorenz flows
We study the expansion properties of the contracting Lorenz flow introduced
by Rovella via thermodynamic formalism. Specifically, we prove the existence of
an equilibrium state for the natural potential for the contracting Lorenz flow and for in an interval
containing . We also analyse the Lyapunov spectrum of the flow in terms
of the pressure
Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities
We consider a class of piecewise smooth one-dimensional maps with critical
points and singularities (possibly with infinite derivative). Under mild
summability conditions on the growth of the derivative on critical orbits, we
prove the central limit theorem and a vector-valued almost sure invariance
principle. We also obtain results on decay of correlations.Comment: 18 pages, minor revisions, to appear in Communications in
Mathematical Physic
Robust exponential decay of correlations for singular-flows
We construct open sets of Ck (k bigger or equal to 2) vector fields with
singularities that have robust exponential decay of correlations with respect
to the unique physical measure. In particular we prove that the geometric
Lorenz attractor has exponential decay of correlations with respect to the
unique physical measure.Comment: Final version accepted for publication with added corrections (not in
official published version) after O. Butterley pointed out to the authors
that the last estimate in the argument in Subsection 4.2.3 of the previous
version is not enough to guarantee the uniform non-integrability condition
claimed. We have modified the argument and present it here in the same
Subsection. 3 figures, 34 page