Journal of the Mathematical Society of Japan

On bifurcations of cusps

Zbigniew SZAFRANIEC

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Abstract

Let $F_t$, where $t \in \mathbb{R}$, be an analytic family of plane-to-plane mappings with $F_0$ having a critical point at the origin. The paper presents effective algebraic methods of computing the number of those cusp points of $F_t$, where $0 < |t|\ll 1$, emanating from the origin at which $F_t$ has a positive/negative local topological degree.

Article information

Source
J. Math. Soc. Japan, Volume 71, Number 2 (2019), 555-567.

Dates
Received: 8 November 2017
First available in Project Euclid: 25 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1551085236

Digital Object Identifier
doi:10.2969/jmsj/79217921

Mathematical Reviews number (MathSciNet)
MR3943450

Zentralblatt MATH identifier
07090055

Subjects
Primary: 14P15: Real analytic and semianalytic sets [See also 32B20, 32C05]
Secondary: 58K05: Critical points of functions and mappings

Keywords
singularities bifurcations cusps

Citation

SZAFRANIEC, Zbigniew. On bifurcations of cusps. J. Math. Soc. Japan 71 (2019), no. 2, 555--567. doi:10.2969/jmsj/79217921. https://projecteuclid.org/euclid.jmsj/1551085236


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