Puiseux series polynomial dynamics and iteration of complex cubic polynomials
نویسندگان
چکیده
منابع مشابه
Puiseux Series Polynomial Dynamics and Iteration of Complex Cubic Polynomials
We study polynomials with coefficients in a field L as dynamical systems where L is any algebraically closed and complete ultrametric field with dense valuation group and characteristic zero residual field. We give a complete description of the dynamical and parameter space of cubic polynomials. In particular we characterize cubic polynomials with compact Julia sets. Also, we prove that any inf...
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We prove that the binary complexity of solving ordinary polynomial differential equations in terms of Puiseux series is single exponential in the number of terms in the series. Such a bound was given in 1990 by Grigoriev for Riccatti differential polynomials associated to ordinary linear differential operators. In this paper, we get the same bound for arbitrary differential polynomials. The alg...
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2. PAYrERNS ........................... 235 Topological preliminaries .................... 235 C o n s t r u c t i n g the t ree o f p a t t e r n s . . . . . . . . . . . . . . . . 237 T he po ten t i a l func t ion hR . . . . . . . . . . . . . . . . . . . . 239 Cri t ical g raphs , annul i and a r g u m e n t s . . . . . . . . . . . . . 240 T h e t ree o f real p a t t e r n s . . . . . . . . ...
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We have designed a new symbolic-numeric strategy to compute efficiently and accurately floating point Puiseux series defined by a bivariate polynomial over an algebraic number field. In essence, computations modulo a well chosen prime number p are used to obtain the exact information needed to guide floating point computations. In this paper, we detail the symbolic part of our algorithm: First ...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2006
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2215