Constructing locally connected non-computable Julia sets

Mark Braverman; Michael Yampolsky

doi:10.1007/s00220-009-0858-5

Constructing locally connected non-computable Julia sets

Mark Braverman, Michael Yampolsky

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

7 Scopus citations

Abstract

A locally connected quadratic Siegel Julia set has a simple explicit topological model. Such a set is computable if there exists an algorithm to draw it on a computer screen with an arbitrary resolution. We constructively produce parameter values for Siegel quadratics for which the Julia sets are non-computable, yet locally connected.

Original language	English (US)
Pages (from-to)	513-532
Number of pages	20
Journal	Communications In Mathematical Physics
Volume	291
Issue number	2
DOIs	https://doi.org/10.1007/s00220-009-0858-5
State	Published - 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-009-0858-5

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title = "Constructing locally connected non-computable Julia sets",

abstract = "A locally connected quadratic Siegel Julia set has a simple explicit topological model. Such a set is computable if there exists an algorithm to draw it on a computer screen with an arbitrary resolution. We constructively produce parameter values for Siegel quadratics for which the Julia sets are non-computable, yet locally connected.",

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AU - Yampolsky, Michael

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AB - A locally connected quadratic Siegel Julia set has a simple explicit topological model. Such a set is computable if there exists an algorithm to draw it on a computer screen with an arbitrary resolution. We constructively produce parameter values for Siegel quadratics for which the Julia sets are non-computable, yet locally connected.

UR - https://www.scopus.com/pages/publications/70349904234

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U2 - 10.1007/s00220-009-0858-5

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M3 - Article

AN - SCOPUS:70349904234

SN - 0010-3616

VL - 291

SP - 513

EP - 532

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 2

ER -

Constructing locally connected non-computable Julia sets

Abstract

All Science Journal Classification (ASJC) codes

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