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Milnor’s attractors persistent recurrence and renormalization. (English) Zbl 0797.58050
Goldberg, Lisa R. (ed.) et al., Topological methods in modern mathematics. Proceedings of a symposium in honor of John Milnor’s sixtieth birthday, held at the State University of New York at Stony Brook, USA, June 14-June 21, 1991. Houston, TX: Publish or Perish, Inc. 513-541 (1993).
In the work of J. Milnor [Commun. Math. Phys. 99, 177-195 (1985; Zbl 0595.58028) and ibid. 102, 517-519 (1985; Zbl 0602.58030)] a new version of the concept of attractor is given and the problem of the structure of the global attractor for one-dimensional maps is stated. The article under review contains the solution of this problem for quasiquadratic maps ($$S$$-unimodal maps with nondegenerate critical points).
For the entire collection see [Zbl 0780.00031].

##### MSC:
 37C70 Attractors and repellers of smooth dynamical systems and their topological structure
##### Keywords:
global attractor; one-dimensional maps; quasiquadratic maps