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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.29 no.3 Antofagasta Dec. 2010

http://dx.doi.org/10.4067/S0716-09172010000300007 

Proyecciones Journal of Mathematics
Vol. 29, N° 3, pp. 241-289, December 2010.
Universidad Católica del Norte
Antofagasta - Chile


BIFURCATION OF THE ESSENTIAL DYNAMICS OF LORENZ MAPS ON THE REAL LINE AND THE BIFURCATION SCENARIO FOR LORENZ LIKE FLOWS : THE CONTRACTING CASE *


Rafael Labarca1
Carlos Moreira2

1Universidad de Santiago de Chile, Chile
2I. M. P. A., Brasil



Correspondencia a:


Abstract

In this article we provide, by using kneading sequences, the combinatorial bifurcation diagram associated to a typical two parameter family of contracting Lorenz maps on the real line. We apply these results to two parameter families of geometric Lorenz-like flows.

Keywords : Lorenz maps; combinatorial bifurcation diagramme; lexicographical world, geometric Lorenz-like flows.

Mathematics Subject Classification 2010 : Primary: 37010, 37C10, 37E05. Secondary : 37C20.



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R. Labarca
Departamento de Matematica y Ciencias de la Computación
Universidad de Santiago de Chile
Casilla 307 Correo 2
Santiago
e-mail : rafael.labarca@usach.cl


C. Moreira
I. M. P. A.
Estrada Dona Castorina 110
CEP 22460-320
Jardim Botanico
Rio de Janeiro
Brazil
e-mail : gugu@impa.br


Received : October 2010. Accepted : November 2010

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