Communications in Mathematical Physics

, Volume 211, Issue 3, pp 527-558

First online:

Strange Attractors Across the Boundary¶of Hyperbolic Systems

  • C. A. MoralesAffiliated withDepartamento de Métodos Matemáticos, IM-UFRJ, Caixa Postal 68530, Cep 21945-970, Rio de Janeiro, RJ, Brasil. E-mail: morales@impa.br; enrique@impa.br; pacifico@impa.br
  • , M. J. PacificoAffiliated withDepartamento de Métodos Matemáticos, IM-UFRJ, Caixa Postal 68530, Cep 21945-970, Rio de Janeiro, RJ, Brasil. E-mail: morales@impa.br; enrique@impa.br; pacifico@impa.br
  • , E. R. PujalsAffiliated withDepartamento de Métodos Matemáticos, IM-UFRJ, Caixa Postal 68530, Cep 21945-970, Rio de Janeiro, RJ, Brasil. E-mail: morales@impa.br; enrique@impa.br; pacifico@impa.br

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Abstract:

We study a bifurcation of Axiom A (hyperbolic) vector fields in dimension three leading to robust strange attractors with singularities. The Axiom A vector fields involved in the bifurcation exhibit a basic set equivalent to the suspension of a three symbol subshift. The attractors arising from this kind of bifurcation are not equivalent to the geometric Lorenz attractors.