Existence, nonexistence and universal breakdown of dissipative golden invariant tori. III. Invariant circles for mappings of the annulus

摘要

For pt.II see ibid. vol.5, p.663-680 (1992). In this series of three papers the author rigorously formulates and proves a number of the main conjectures associated with renormalization of golden-mean quasi-periodic dynamical systems. In particular, in the previous two papers, he proved the existence of an open set of families of analytic mappings of the circle with the universal properties described in earlier papers and studied the definition and convergence of renormalization operators for dissipative annulus mappings. In this final paper, he formulates and proves general results about when convergence of renormalization implies existence of an invariant circle and then describes part of the boundary of the set of dissipative diffeomorphisms of the annulus and its universal structure.