Dynamical Systems Seminar

主講者: Prof. Atsuro Sannami (Kitami Institute of Technology)
講題: Coding of Dynamical Systems and a Sufficient Condition for Non-existence of Finite-to-One Symbolic Extensions
時間: 2007-12-19 (Wed.)  15:00-16:00
地點:
Abstract:  I will give a review on symbolic representation of dynamical systems. I will show the ideas of generating partition, pruning front and symbolic extension. I will prove that if a homeomorphism on a compact metric space has a periodic orbit having an accumulating invariant sets, then it cannot have any finite-to-one symbolic extension. We can apply this result for symplectic diffeomorphisms on the plane having a stable elliptic periodic point. There are invariant circles around it, and therefore they cannot have any finite-to-one symbolic extension. Area-preserving Henon map is an interesting example. A calculation of the 1st coefficient of the Birkhoff normal form of its elliptic fixed point shows that the area-preserving Henon map cannot have any finite-to-one symbolic extension on a parameter interval except for some specific 3-values.
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