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Download Citation on ResearchGate | Invariant factors, Julia equivalences and the (Abstract) Mandelbrot set / Karsten Keller | Incluye bibliografía e índice.
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Lectures notes

See our disclaimer. Invariant Factors, Julia Equivalences and the Abstract Mandelbrot Set This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. This restriction preserves the most essential properties of the subject, but drastically simplifies computer simulations and the mathematical formalism. The coverage includes a basic description of the structure of the set of orbits and pre-orbits associated with any map of an analytic space into itself.


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A detailed study of the space of orbits the algebraic Julia set as a whole, together with related attributes, is provided. Also covered are: moduli space in the space of maps and the classification problem for analytic maps, the relation of the moduli space to the bifurcations topology changes of the set of orbits, a combinatorial description of the moduli space Mandelbrot and secondary Mandelbrot sets and the corresponding invariants discriminants and resultants , and the construction of the universal discriminant of analytic functions in terms of series coefficients. The book concludes by solving the case of the quadratic map using the theory and methods discussed earlier.

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