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Checkerboard Julia sets for rational maps

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dc.contributor.author Blanchard, Paul
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.date.accessioned 2017-03-14T11:24:26Z
dc.date.available 2017-03-14T11:24:26Z
dc.date.issued 2013-02
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 tr_TR
dc.identifier.issn 0218-1274
dc.identifier.uri http://hdl.handle.net/20.500.12416/1465
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. tr_TR
dc.language.iso eng tr_TR
dc.publisher World Scientific Publ. tr_TR
dc.relation.isversionof 10.1142/S0218127413300048 tr_TR
dc.rights info:eu-repo/semantics/openAccess
dc.subject Julia Set tr_TR
dc.subject Mandelbrot Set tr_TR
dc.subject Symbolic Dynamics tr_TR
dc.title Checkerboard Julia sets for rational maps tr_TR
dc.type article tr_TR
dc.relation.journal International Journal Of Bifurcation And Chaos tr_TR
dc.identifier.volume 23 tr_TR
dc.identifier.issue 2 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü tr_TR


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