Feigenbaum theory for unimodal maps with asymmetric critical point: Rigorous results

B. D. Mestel; A. H. Osbaldestin

doi:10.1007/s002200050448

Feigenbaum theory for unimodal maps with asymmetric critical point: Rigorous results

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 apply the methods of H. Epstein to prove the existence of a line of period-2 solutions of the Feigenbaum period-doubling renormalisation transformation. These solutions govern the universal behaviour of families of unimodal maps with "asymmetric critical points" of degree d, for which the d^th derivative has differing left and right limits.

Original language	English
Pages (from-to)	211-228
Number of pages	18
Journal	Communications in Mathematical Physics
Volume	197
Issue number	1
DOIs	https://doi.org/10.1007/s002200050448
Publication status	Published - 1 Jan 1998

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title = "Feigenbaum theory for unimodal maps with asymmetric critical point: Rigorous results",

abstract = "We apply the methods of H. Epstein to prove the existence of a line of period-2 solutions of the Feigenbaum period-doubling renormalisation transformation. These solutions govern the universal behaviour of families of unimodal maps with {"}asymmetric critical points{"} of degree d, for which the dth derivative has differing left and right limits.",

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AB - We apply the methods of H. Epstein to prove the existence of a line of period-2 solutions of the Feigenbaum period-doubling renormalisation transformation. These solutions govern the universal behaviour of families of unimodal maps with "asymmetric critical points" of degree d, for which the dth derivative has differing left and right limits.

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

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Feigenbaum theory for unimodal maps with asymmetric critical point: Rigorous results

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