The Mandelbrot set is the shadow of a Julia set
Copyright policy )The Mandelbrot set is the shadow of a Julia set
Working within the polynomial quadratic family, we introduce a new point of view on bifurcations which naturally allows to see the seat of bifurcations as the projection of a Julia set of a complex dynamical system in dimension three. We expect our approach to be extendable to other holomorphic families of dynamical systems.
Equilibrium measure, 330, Mathematics - Complex Variables, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Combinatorics and topology in relation with holomorphic dynamical systems, Julia set, Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables, Dynamical Systems (math.DS), Green current, 004, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets, bifurcation, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], Mandelbrot set, FOS: Mathematics, Bifurcation, Mathematics - Dynamical Systems, Complex Variables (math.CV), equilibrium measure, equilibrium measure CONTENTS
Equilibrium measure, 330, Mathematics - Complex Variables, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Combinatorics and topology in relation with holomorphic dynamical systems, Julia set, Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables, Dynamical Systems (math.DS), Green current, 004, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets, bifurcation, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], Mandelbrot set, FOS: Mathematics, Bifurcation, Mathematics - Dynamical Systems, Complex Variables (math.CV), equilibrium measure, equilibrium measure CONTENTS
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