The existence of smooth families of Lorenz maps exhibiting all possible
dynamical behavior is established and the structure of the parameter space of
these families is described

de Melo, Welington

Martens, Marco

English

arXiv

.  The existence of smooth families of Lorenz maps exhibiting all possible dynamical behavior is established and the structure of the parameter space of these families is described. 1  Institute of Mathematical Sciences, SUNY at Stony Brook, Stony Brook, NY 11794-3651.  2  IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil. Typeset by A M S-T E X  1. Introduction The aim of this paper is to exhibit some parameterized families of Lorenz flows that are topologically universal in the sense that given any geometric Lorenz flow, its dynamics is essentially the same as the dynamics of some element of the family. Thus, these families plays, in the context of Lorenz flows, the same role as the quadratic family in the context of unimodal interval maps. Lorenz in [L] showed numerically the existence of some flows in three dimension that have complicated recurrent behavior. What we now call a Lorenz flow has a singularity of saddle type with a one dimensional unstable manifold an..

Marco Martens

Welington De Melo

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Universal Models For Lorenz Maps

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.1419

Universal models for Lorenz maps

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