Infinitely many periodic attractors for holomorphic maps of 2 variables. (English) Zbl 0878.58044

Buzzard, Gregery T.

Ann. Math. (2) 145, No. 2, 389-417 (1997).

The important development in the study of discrete dynamical systems was Newhouse’s use of persistent homoclinic tangencies to show that a large set of \(C^2\)-diffeomorphisms of compact surfaces have infinitely many coexisting periodic attractors, or sinks [S. E. Newhouse, Prog. Math. 8, 1-114 (1980; Zbl 0444.58001)]. In the present article this result is obtained for various spaces of holomorphic maps of two variables.

Reviewer: B.V.Loginov (Ul’yanovsk)

MSC:

37C70

Attractors and repellers of smooth dynamical systems and their topological structure

Keywords:

discrete dynamical systems; coexisting periodic attractors; sinks; holomorphic maps

Citations:

Zbl 0444.58001