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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].

##### MSC:
 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 54H20 Topological dynamics (MSC2010) 37E99 Low-dimensional dynamical systems
##### Keywords:
periodic orbit; homeomorphism; two-dimensional disk; cycle