Renormalisation in a circle map with two inflection points

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

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

Fingerprint

Circle Map
Point of inflection
inflection points
Renormalization
Orbits
Orbit
orbits
Quasiperiodicity
operators
Equivalence relation
Operator
Chaos theory
Universality
equivalence
Parameter Space
chaos
Critical point
critical point
Chaos
High-dimensional

Cite this

@article{194f000d41ae4ee4a9db9c5ad2660e01,
title = "Renormalisation in a circle map with two inflection points",
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.",
author = "Ketoja, {Jukka A.}",
year = "1992",
month = "1",
day = "1",
doi = "10.1016/0167-2789(92)90187-R",
language = "English",
volume = "55",
pages = "45--68",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "1-2",

}

Renormalisation in a circle map with two inflection points. / Ketoja, Jukka A.

In: Physica D: Nonlinear Phenomena, Vol. 55, No. 1-2, 01.01.1992, p. 45-68.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Renormalisation in a circle map with two inflection points

AU - Ketoja, Jukka A.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=29044443293&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(92)90187-R

DO - 10.1016/0167-2789(92)90187-R

M3 - Article

AN - SCOPUS:29044443293

VL - 55

SP - 45

EP - 68

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -