Geometry and Algebra of the Deltoid Map

2020/05/11 by Bowman, Joshua P.
#37F10 (Primary) 37F20 #53A04 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2005.05461

Abstract

The geometry of the deltoid curve gives rise to a self-map of ℂ² that is expressed in coordinates by f(x,y) = (y² - 2x, x² - 2y). This is one in a family of maps that generalize Chebyshev polynomials to several variables. We use this example to illustrate two important objects in complex dynamics: the Julia set and the iterated monodromy group.

Related

• Hypergroup properties for the deltoid model
• Combinatorics and topology of straightening maps I: compactness and bijectivity
• Iterated monodromy groups of Chebyshev-like maps on ℂⁿ
• Polynomial semiconjugacies, decompositions of iterations, and invariant\n curves
• A computation of invariants of a rational self-map