Document Type
Article
Publication Date
1996
Abstract
In this paper we are concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or ‘‘eruption,’’ is described. A fundamental role is played by the interactions of fixed points and singular curves. Other critical elements in the phase space include periodic points and an invariant line. The dynamics along the invariant line, in two of the examples, reduces to the one-dimensional Newton’s method which is conjugate to a degree two rational map. We also determine, computationally, the characteristic exponents for all of the systems. An unexpected coincidence is that the parameter range where the invariant line becomes neutrally stable, as measured by a zero Lyapunov exponent, coincides with the merging of a periodic point with a point on a singular curve.
DOI
10.1063/1.166158
MSU Digital Commons Citation
Billings, Lora and Curry, James H., "On noninvertible mappings of the plane: Eruptions" (1996). Department of Mathematics Facuty Scholarship and Creative Works. 23.
https://digitalcommons.montclair.edu/mathsci-facpubs/23
Published Citation
Billings, L., & Curry, J. H. (1996). On noninvertible mappings of the plane: Eruptions. Chaos, 6(2), 108-120. doi:10.1063/1.166158
Comments
The following article appeared in Chaos (ISSN: 1054-1500, ESSN: 1089-7682), and may be found at https://doi.org/10.1063/1.166158. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.