Speaker : Prof. Ken Palmer (Monash University)
Title : Shadowing, Homoclinic Orbits and Chaos
Time : 2014-12-12 (Fri) 15:30 - 16:30
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: We review the shadowing theorem for compact hyperbolic sets of a diffeomorphism. Then we discuss the recent result of Pilyugin and Tikhomirov that Lipschitz shadowing implies hyperbolicity. We show how shadowing can be used to prove the existence of chaotic dynamics in the neighbourhood of a transversal homoclinic orbit. Next we show how shadowing techniques can be used to give computer-assisted proofs of the existence of transversal homoclinic orbits.