On the existence of fixed points of the composition operator for circle maps

DOI10.1007/BF01209392zbMath0603.58004MaRDI QIDQ1082659

Jean-Pierre Eckmann, Henri Epstein

Publication date: 1986

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

fixed pointscomposition operatorgolden ratio rotation numberwide range

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point theorems on manifolds (58C30)

Related Items

On analytic perturbations of a family of Feigenbaum-like equations ⋮ Single-valley-extended solutions with platforms of FKS equation ⋮ Analytic Solutions of the Cvitanović–Feigenbaum and Feigenbaum–Kadanoff–Shenker Equations ⋮ Single-valley solutions of the second type of FKS equation ⋮ Differentiable solutions of the Feigenbaum-Kadanoff-Shenker equation ⋮ Regularity of Conjugacies between Critical Circle Maps: An Experimental Study ⋮ The dimension spectrum of some dynamical systems

Cites Work

• Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
• Universal properties of maps of the circle with \(\epsilon\)-singularities
• Functional equations for circle homeomorphisms with golden ratio rotation number
• New proofs of the existence of the Feigenbaum functions
• Analyticity properties of the Feigenbaum function