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Fundamental regions of planar homeomorphisms. (English) Zbl 0732.54029

Continuum theory and dynamical systems, Proc. AMS-IMS-SIAM Jt. Summer Res. Conf., Arcata/CA (USA) 1989, Contemp. Math. 117, 49-56 (1991).
[For the entire collection see Zbl 0723.00027.]
Basic to the study of planar homeomorphisms are the papers of L. E. J. Brouwer [Beweis des ebenen Translationssatzes, Math. Ann. 72, 37-54 (1912)] and S. A. Andrea [Abh. Math. Semin. Univ. Hamb. 30, 61-74 (1967; Zbl 0156.437)], the methods of these papers are summarized and then techniques are devised to construct homeomorphisms with pathological fundamental region structures. In particuar a Brouwer homeomorphism is described which is not invariant on any closed line.
Reviewer: W.R.Utz (Columbia)

MSC:

54F15 Continua and generalizations
37-XX Dynamical systems and ergodic theory