Renormalisation in implicit complex maps

B. D. Mestel; A. H. Osbaldestin

doi:10.1016/0167-2789(89)90001-8

Renormalisation in implicit complex maps

B. D. Mestel^*, A. H. Osbaldestin

^*Corresponding author for this work

School of Mathematics & Physics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the dynamics of a family of implicit complex maps restricted to an invariant circle. The renormalisation analysis for golden mean rotation number is given. We find a one-parameter family of universality classes and relate this to a line of fixed points of the square of the circle map renormalisation transformation. These period-2 points are pairs of fractional linear maps.

Original language	English
Pages (from-to)	149-162
Number of pages	14
Journal	Physica D: Nonlinear Phenomena
Volume	39
Issue number	2-3
DOIs	https://doi.org/10.1016/0167-2789(89)90001-8
Publication status	Published - 2 Oct 1989

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title = "Renormalisation in implicit complex maps",

abstract = "We study the dynamics of a family of implicit complex maps restricted to an invariant circle. The renormalisation analysis for golden mean rotation number is given. We find a one-parameter family of universality classes and relate this to a line of fixed points of the square of the circle map renormalisation transformation. These period-2 points are pairs of fractional linear maps.",

author = "Mestel, {B. D.} and Osbaldestin, {A. H.}",

year = "1989",

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AB - We study the dynamics of a family of implicit complex maps restricted to an invariant circle. The renormalisation analysis for golden mean rotation number is given. We find a one-parameter family of universality classes and relate this to a line of fixed points of the square of the circle map renormalisation transformation. These period-2 points are pairs of fractional linear maps.

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U2 - 10.1016/0167-2789(89)90001-8

DO - 10.1016/0167-2789(89)90001-8

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SP - 149

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 2-3

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Renormalisation in implicit complex maps

Abstract

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