Symmetric Heteroclinic Connections in the Michelson System: A Computer Assisted Proof
- 1 January 2005
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Dynamical Systems
- Vol. 4 (3) , 489-514
Abstract
In this paper we present a new technique of proving the existence of an infinite number of symmetric heteroclinic and homoclinic solutions. This technique combines the covering relations method introduced by Zgliczynski [Topol. Methods Nonlinear Anal., 8 (1996), pp. 169--177; Nonlinearity, 10 (1997), pp. 243--252] with symmetry properties of a dynamical system. As an example we present a computer assisted proof of the existence of an infinite number of heteroclinic connections between equilibrium points in the Kuramoto--Sivashinsky ODE [D. Michelson, Phys. D, 19 (1986), pp. 89--111]. Moreover, we present the proof of the existence of an infinite number of heteroclinic connections between periodic orbits and equilibrium points.Keywords
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