Seminar on Dynamic Systems
主講者: Prof. Ken Palmer (Monash University)
講題: Shadowing, Homoclinic Orbits and Chaos
時間: 2014-12-12 (Fri.)  15:30 - 16:30
地點: 數學所 722 研討室 (台大院區)
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.
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