A Shil'nikov's theorem in an extended neighborhood of a saddle point of focus - focus type in banach spaces

• Maturana, Ana María ^[1]
  1. [1] Universidad Técnica Federico Santa María.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 16, Nº. 2, 1997, págs. 157-180
• Idioma: inglés
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• Resumen

  • In this work, we will study the existence of chaotic solutions in an extended neighborhood of a homoclinic orbit for a kind of evolutions equations in Banach spaces of infinite dimension. First, we will prove that the solutions admit an exponential expansion and then we will imply the existence of a subsystem of solutions which is in one-to-one correspondence with the set of doubly infinite sequences.