A Shil'nikov's theorem in R4 in an extended neighborhood of a saddle point of focus - focus type
DOI:
https://doi.org/10.22199/S07160917.1996.0001.00003Abstract
In this article we study the existence of chaotic solutions in a neighborhood of a homoclinic orbit of a saddle point of focus-focus type. We will prove that the solutions have an exponential expansion, this fact implies the existence of a subsystem of solutions, which is in one-to-one correspondence with the set of doubly infinite sequences.References
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[2] Deng, B. "Exponential expansion with Shil'nikov Saddle- Focus". Journal Differential Equation, 82, 156--173, 1989.
[3] Hale, J. "Ordinary Differential Equations", John Wiley & Sons, Inc, New York, 1969.
[4] Ovsyannikov, l. M. & Shil'nikov, L.P. “On Systems with a Saddle Focus Homoclinic Curve''. Math. USSR Sbornik, Vol. 58, No. 2, 557--574, 1987.
[5] Shil'nikov, L.P. “A case of the existence of a Countable number of Periodic Motions". Soviet Math. Doklady 6, MIR 30 N°3262, 163, 1965.
[6] Shil'nikov, L.P. ''On a Poincaré-Birkhoff problem''. Math USSR Sbornik, Vol. 3, No. 3, 353-371, 1967.
[7] Shil'nikov, L.P. “The existence of a denumerable set of Periodic Motions in four-dimensional space in an extended neighborhood of a Saddle-Focus". Soviet Math. Doklady Vol. 8, No. 1, MR 35 No 1872, 54-58, 1967.
[8] Shil'nikov, L.P. “A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of Saddle-Focus type". Math USSR Sbornik Vol. 10, No. 1, 91-102, 1970.
[9] Tresser, C. "Modèles simples de transitious vers la turbulence", Doctorat D'Etat, Université de Nice, 1981.
Published
2018-04-04
How to Cite
[1]
A. M. Maturana, “A Shil’nikov’s theorem in R4 in an extended neighborhood of a saddle point of focus - focus type”, Proyecciones (Antofagasta, On line), vol. 15, no. 1, pp. 29-45, Apr. 2018.
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