Renormalisation in a circle map with two inflection points

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Abstract

An extended version of the sine circle map becomes non-invertible by developing simultaneously two critical points in part of parameter space. Universality in the corresponding transition from quasiperiodicity to chaos manifests itself in the organisation of doubly superstable orbits. Four operators are needed to generate all such orbits. The existence of non-trivial equivalence relations for operation sequences makes the present theory different from other multi-operator renormalisation approaches. Possible implications of the theory in higher-dimensional systems are discussed.

Original languageEnglish
Pages (from-to)45-68
Number of pages24
JournalPhysica D: Nonlinear Phenomena
Volume55
Issue number1-2
DOIs
Publication statusPublished - 1 Jan 1992
MoE publication typeNot Eligible

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