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Checkerboard Julia sets for rational maps

dc.contributor.author Çilingir, Figen
dc.contributor.author Çilingir, Figen
dc.contributor.author Cuzzocreo, Daniel
dc.contributor.author Devaney, Robert L.
dc.contributor.author Look, Daniel M.
dc.contributor.author Russell, Elizabeth D.
dc.contributor.other Matematik
dc.date.accessioned 2017-03-14T11:24:26Z
dc.date.available 2017-03-14T11:24:26Z
dc.date.issued 2013
dc.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü en_US
dc.description.abstract In this paper, we consider the family of rational maps F-lambda(z) = z(n) + lambda/z(d), where n >= 2, d >= 1, and lambda is an element of C. We consider the case where lambda lies in the main cardioid of one of the n - 1 principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic. However, two such maps F-lambda and F-mu are conjugate on these Julia sets only if the parameters at the centers of the given cardioids satisfy mu = nu(j(d+1))lambda or mu = nu(j(d+1))(lambda) over bar where j is an element of Z and nu is an (n - 1)th root of unity. We define a dynamical invariant, which we call the minimal rotation number. It determines which of these maps are conjugate on their Julia sets, and we obtain an exact count of the number of distinct conjugacy classes of maps drawn from these main cardioids. en_US
dc.description.publishedMonth 2
dc.identifier.citation Blanchard, P...et al. (2013). Checkerboard Julia sets for rational maps. International Journal Of Bifurcation And Chaos, 23(2). http://dx.doi.org/10.1142/S0218127413300048 en_US
dc.identifier.doi 10.1142/S0218127413300048
dc.identifier.issn 0218-1274
dc.identifier.issue 2 en_US
dc.identifier.uri https://hdl.handle.net/20.500.12416/1465
dc.identifier.volume 23 en_US
dc.language.iso en en_US
dc.publisher World Scientific Publ. en_US
dc.relation.ispartof International Journal Of Bifurcation And Chaos en_US
dc.rights info:eu-repo/semantics/openAccess en_US
dc.subject Julia Set en_US
dc.subject Mandelbrot Set en_US
dc.subject Symbolic Dynamics en_US
dc.title Checkerboard Julia sets for rational maps tr_TR
dc.title Checkerboard Julia Sets for Rational Maps en_US
dc.type Article en_US
dspace.entity.type Publication
relation.isAuthorOfPublication 245a2c09-a006-4375-84aa-393bc52526e3
relation.isAuthorOfPublication.latestForDiscovery 245a2c09-a006-4375-84aa-393bc52526e3
relation.isOrgUnitOfPublication 26a93bcf-09b3-4631-937a-fe838199f6a5
relation.isOrgUnitOfPublication.latestForDiscovery 26a93bcf-09b3-4631-937a-fe838199f6a5

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