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Iteration of Contractions and Analytic Maps
Journal of the London Mathematical Society, 1990The Denjoy-Wolff theorem states that if f is an analytic map of the unit disc into itself, then the iterates \(f^ n\) converge to some point in the closure of the unit disc. Excluding Möbius maps, each f is a contraction with respect to the hyperbolic metric. The result is generalized to contractions of Hadamard and visibility n-dimensional manifolds.
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2000
Abstract Dynamical systems described by iterated map functions are used to explore the period-doubling route to chaos, Lyapunov exponents, and Feigenbaum numbers. A simple derivation of the numerical value of the Feigenbaum number α is provided.
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Abstract Dynamical systems described by iterated map functions are used to explore the period-doubling route to chaos, Lyapunov exponents, and Feigenbaum numbers. A simple derivation of the numerical value of the Feigenbaum number α is provided.
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Fractional iterates for n-dimensional maps
Applied Mathematics and Computation, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Iterates of Maps with Symmetry
SIAM Journal on Mathematical Analysis, 1988In this paper the elementary aspects of bifurcation of fixed points, period doubling, and Hopf bifurcation for iterates of equivariant mappings are discussed. The most interesting of these is an algebraic formulation of the hypotheses of Ruelle’s theorem (D. Ruelle [1973], “Bifurcations in the presence of a symmetry group,” Arch. Rational Mech.
Pascal Chossat, Martin Golubitsky
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2000
The local study of iterated holomorphic mappings, in a neighborhood of a fixed point, was quite well developed in the late 19th century. (Compare §§8–10, and see Alexander.) However, except for one very simple case studied by Schroder and Cayley (see Problem 7-a), nothing was known about the global behavior of iterated holomorphic maps until 1906, when
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The local study of iterated holomorphic mappings, in a neighborhood of a fixed point, was quite well developed in the late 19th century. (Compare §§8–10, and see Alexander.) However, except for one very simple case studied by Schroder and Cayley (see Problem 7-a), nothing was known about the global behavior of iterated holomorphic maps until 1906, when
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Making a Pangenome Using the Iterative Mapping Approach
Methods in Molecular Biology, 2022Cassandria G Tay Fernández
exaly
2001
To introduce simple complex iterative maps. To introduce Julia sets, the Mandelbrot set, and Newton fractals. To carry out some analysis on these sets.
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To introduce simple complex iterative maps. To introduce Julia sets, the Mandelbrot set, and Newton fractals. To carry out some analysis on these sets.
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