REAL-ANALYTICITY OF HAUSDORFF DIMENSION OF JULIA SETS ALONG THE PARABOLIC ARCS OF THE MULTICORNS

摘要: SABYASACHI MUKHERJEEAbstract. In this article, we take a dimension-theoretic look at the connect-edness loci of unicritical anti-polynomials, known as multicorns and provea regularity property Hausdorff dimension Julia sets on per-sistently parabolic part these parameter spaces.The boundaries odd period hyperbolic components multicornscontain real-analytic arcs consisting quasi-conformally conjugate parabolicparameters. The principal result paper asserts that di-mension is function alongthese arcs. We also prove, along way, dynamically nat-ural parametrization has non-vanishing derivative allbut (possibly) finitely many points.Our main remains true for more general provided allthe active critical points converge to attracting or cycles.