On bifurcation of cusps
Zbigniew Szafraniec
TL;DR
This paper introduces effective methods to compute the number of cusps with positive or negative cusp degree that emerge from the origin in an analytic family of plane-to-plane mappings near a parameter value of zero.
Contribution
It provides novel computational techniques for analyzing cusp bifurcations in analytic plane mappings, focusing on cusps emanating from the origin.
Findings
Methods for counting cusps with positive cusp degree
Methods for counting cusps with negative cusp degree
Application to bifurcation analysis of plane-to-plane mappings
Abstract
Let f_t , where t is close to zero, be an analytic family of plane-to-plane mappings. There are presented effective methods of computing the number of cusps of f_t emanating from the origin and having positive/negative cusp degree.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Analytic and geometric function theory · Functional Equations Stability Results