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Full-Text Articles in Physical Sciences and Mathematics
Asymptotic Invariants And Flatness Of Local Endomorphisms, Nikita Miasnikov
Asymptotic Invariants And Flatness Of Local Endomorphisms, Nikita Miasnikov
Dissertations, Theses, and Capstone Projects
For a local endomorphism of a noetherian local ring we introduce 3 asymptotic invariants one of which we call entropy. We use this notion of entropy to extend numerical conditions in Kunz' regularity criterion to every contracting endomorphism of a noetherian local ring, and to give a characteristic-free interpretation of the definition of Hilbert-Kunz multiplicity. We also show that every finite endomorphism of a complete noetherian local ring of equal characteristic can be lifted to a finite endomorphism of a complete regular local ring. The local ring of an algebraic or analytic variety at a point fixed by a finite …
On The Dynamics Of Quasi-Self-Matings Of Generalized Starlike Complex Quadratics And The Structure Of The Mated Julia Sets, Ross Flek
Dissertations, Theses, and Capstone Projects
It has been shown that, in many cases, Julia sets of complex polynomials can be "glued" together to obtain a new Julia set homeomorphic to a Julia set of a rational map; the dynamics of the two polynomials are reflected in the dynamics of the mated rational map. Here, I investigate the Julia sets of self-matings of generalized starlike quadratic polynomials, which enjoy relatively simple combinatorics. The points in the Julia sets of the mated rational maps are completely classified according to their topology. The presence and location of buried points in these Julia sets are addressed. The interconnections between …