Entropy and rotation intervals for circle maps near saddle-node bifurcations
Copyright policy )Entropy and rotation intervals for circle maps near saddle-node bifurcations
This paper is devoted to dynamical properties of a one-parameter family of \(C^r\) endomorphisms \(f_\lambda\) of the circle. To this end a formulation of the rotation interval and topological entropy are discussed. The author shows that (admitting that \(f_\lambda\) exhibits nontrivial behaviour) the topological entropy and the width of the rotation interval of \(f_\lambda\) satisfy certain scaling laws as \(\lambda\downarrow 0\) and gives estimates for each of these characteristics.
- Northwestern University United States
- GEORGIA TECH RESEARCH CORPORATION United States
- NORTHWESTERN UNIVERSITY United States
Rotation numbers and vectors, Bifurcations of singular points in dynamical systems, Topological entropy, Differentiable maps on manifolds, rotation interval, topological entropy, Dynamical systems involving maps of the circle, endomorphisms of circle, saddle-node bifurcation
Rotation numbers and vectors, Bifurcations of singular points in dynamical systems, Topological entropy, Differentiable maps on manifolds, rotation interval, topological entropy, Dynamical systems involving maps of the circle, endomorphisms of circle, saddle-node bifurcation
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