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Cycles for disk homeomorphisms and thick trees. (English) Zbl 0793.58029
McCord, Christopher K. (ed.), Nielsen theory and dynamical systems. AMS- IMS-SIAM summer research conference, June 20-26, 1992, South Hadley, MA (USA), supported by the National Science Foundation. Providence, RI: American Mathematical Society. Contemp. Math. 152, 69-139 (1993).
Let \(f\) be an orientation preserving homeomorphism of the two-dimensional disk. The authors fix a cycle (periodic orbit) of \(f\) and describe an algorithm which either produces a tree map with some extra structure (which carries a great deal of dynamical information about \(f\), especially about the existence of other cycles) or reduces the investigation of \(f\) to two simpler homeomorphisms.
For the entire collection see [Zbl 0780.00035].

37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
54H20 Topological dynamics (MSC2010)
37E99 Low-dimensional dynamical systems