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May  2003, 9(3): 505-548. doi: 10.3934/dcds.2003.9.505

Chaotic behaviour of one-dimensional horseshoes

Maria João Costa 1,

1. 

Departamento de Matemática Aplicada, Centro de Matemáplicada, Universidade do Porto, R. do Campo Alegre 687, 4169-007 Porto, Portugal

Received  November 2002 Revised  November 2002 Published  February 2003

We prove that, for an open class of unimodal maps unfolding a saddle-node bifurcation, chaotic behaviour is a prevalent phenomenon: for a set of parameters with positive Lebesgue density at the bifurcation value the maps exhibit a strange attractor.
Keywords: chaotic behaviour., strange attractor, Saddle-node bifurcation.
Mathematics Subject Classification: 37G15, 37D45, 74H60, 74H6.
Citation: Maria João Costa. Chaotic behaviour of one-dimensional horseshoes. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 505-548. doi: 10.3934/dcds.2003.9.505
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