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
• DOI: 10.22199/S07160917.1997.0002.00005
• Enlaces
  • Texto completo
• 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.

• Referencias bibliográficas
  • Citas [1] Blázquez, C. M. "Bifurcation from a homoclinic orbit in parabolic differential equation". Proceedings of the Royal Society...
  • [2] Blázquez, C. M. & Thma, E. "Chaos in infinite dimensions: A generalization of a Theorem of Shil'nikov". Nonlinear Analysis,...
  • [3] Blázquez, C. M. & Turna, E. "Strange Attractors of the Shil'nikov type in Chua's Circuit". International Journal of...
  • [4] Deng, B. "Exponential expansion with Shil'nikov Saddle-Focus". Journal Differential Equation, 82, pp. 156-173, (1989).
  • [5] Henry, D. "Geometry Theory of Semilinear Parabolic Equations '', Lecture Notes in Mathematics, Vol. 840. Springer-Verlag,...
  • [6] Lancaster, P. "Theory of Matrices", Academic Press, San Diego, ( 1969).
  • [7] Ovsyannikov, I. M. & Shil'nikov, L.P. "On Systems with a Saddle-Focus Homoclinic Curve". Math. USSR Sbornik, Vol. 58,...
  • [8] Pazy, A. Semigroups of linear operators and applications to partial differential equations", Applied Mathematical Sciences, Vol. 44,...
  • [9] Shil'nikov, L.P. "On a Poincaré-Birkhoff problem". Math USSR Sbornik, Vol. 3, No. 3, pp. 353-371, (1967).
  • [10] Shil'nikov, L.P. "The existence of a denumerable set of Periodic Motions in four-dimensional space in an extended neighborhood...
  • [11] Shil'nikov, L.P. "A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of...
  • [12] Tresser. C. "Modeles simples de transitions vers la turbulence", Doctorat DEtat, Université de Nice, (1981).