Mixing Rates of the Geometrical Neutral Lorenz Model

Henk Bruin; Hector Homero Canales Farías

doi:10.1007/s10955-023-03212-5

Titel

Mixing Rates of the Geometrical Neutral Lorenz Model

Autor*in

Henk Bruin

Fakultät für Mathematik, Universität Wien

Hector Homero Canales Farías

Fakultät für Mathematik, Universität Wien

Abstract

The aim of this paper is to obtain polynomial decay of correlations of a Lorenz-like flow where the hyperbolic saddle at the origin is replaced by a neutral saddle. To do that, we take the construction of the geometrical Lorenz flow and proceed by changing the nature of the saddle fixed point at the origin by a neutral fixed point. This modification is accomplished by changing the linearised vector field in a neighbourhood of the origin for a neutral vector field. This change in the nature of the fixed point will produce polynomial tails for the Dulac times, and combined with methods of Araújo and Melbourne (used to prove exponential mixing for the classical Lorenz flow) this will ultimately lead to polynomial upper bounds of the decay of correlations for the modified flow.

Stichwort

Polynomial decay of correlationsNeutral geometrical Lorenz flowMixingNeutral fixed point

Objekt-Typ

journal article

Sprache

Englisch [eng]

Persistent identifier

phaidra.univie.ac.at/o:2045018

DOI

10.1007/s10955-023-03212-5

Erschienen in

Titel