Chaotic Behavior in Differential Equations Driven by a Brownian Motion
April 2, 2010
11:00 am 646 PGH
Abstract
In this talk we present a study on the chaotic behavior of ordinary
differential equations with a homoclinic orbit to a dissipative saddle
point under an unbounded random forcing driven by a Brownian motion. We
prove that, for almost all sample pathes of the Brownian motion in the
classical Wiener space, the forced equation admits a topological horseshoe
of infinitely many branches. This result is then applied to the randomly
forced Duffing equation and the pendulum equation.
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