Non computable Mandelbrot-like sets for a one-parameter complex family

Daniel Coronel, Cristobal Rojas, Michael Yampolsky

Resultado de la investigación: Article

Resumen

We show the existence of computable complex numbers λ for which the bifurcation locus of the one-parameter complex family fb(z)=λz+bz2+z3 is not Turing computable.

Idioma originalEnglish
Páginas (desde-hasta)110-122
Número de páginas13
PublicaciónInformation and Computation
Volumen262
DOI
EstadoPublished - 1 oct 2018

Huella dactilar

Turing
Complex number
Locus
Bifurcation
Family

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

Citar esto

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title = "Non computable Mandelbrot-like sets for a one-parameter complex family",
abstract = "We show the existence of computable complex numbers λ for which the bifurcation locus of the one-parameter complex family fb(z)=λz+bz2+z3 is not Turing computable.",
keywords = "Computable complex dynamics, Computational intractability, Mandelbrot set",
author = "Daniel Coronel and Cristobal Rojas and Michael Yampolsky",
year = "2018",
month = "10",
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doi = "10.1016/j.ic.2018.07.003",
language = "English",
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Non computable Mandelbrot-like sets for a one-parameter complex family. / Coronel, Daniel; Rojas, Cristobal; Yampolsky, Michael.

En: Information and Computation, Vol. 262, 01.10.2018, p. 110-122.

Resultado de la investigación: Article

TY - JOUR

T1 - Non computable Mandelbrot-like sets for a one-parameter complex family

AU - Coronel, Daniel

AU - Rojas, Cristobal

AU - Yampolsky, Michael

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We show the existence of computable complex numbers λ for which the bifurcation locus of the one-parameter complex family fb(z)=λz+bz2+z3 is not Turing computable.

AB - We show the existence of computable complex numbers λ for which the bifurcation locus of the one-parameter complex family fb(z)=λz+bz2+z3 is not Turing computable.

KW - Computable complex dynamics

KW - Computational intractability

KW - Mandelbrot set

UR - http://www.scopus.com/inward/record.url?scp=85050826664&partnerID=8YFLogxK

U2 - 10.1016/j.ic.2018.07.003

DO - 10.1016/j.ic.2018.07.003

M3 - Article

VL - 262

SP - 110

EP - 122

JO - Information and Computation

JF - Information and Computation

SN - 0890-5401

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