3 papers
math.DS2017
Affine map equivalence versus critical set equivalence for quadratic maps of the plane
Chia-Hsing Nien, Bruce B. Peckham, Richard P. McGehee
In recent work [Nien et al. 2016], the authors enumerated a classification of quadratic maps of the plane according to their critical sets and images. It is straightforward to show…
math.DS2015
Classification of critical sets and their images for quadratic maps of the plane
Chia-Hsing Nien, Bruce B. Peckham, Richard P. McGehee
We provide a complete classification of the critical sets and their images for quadratic maps of the real plane. Critical sets are always conic sections, which provides a starting…
math.DS2003
A route to computational chaos revisited: noninvertibility and the breakup of an invariant circle
Christos E. Frouzakis, Ioannis G. Kevrekidis, Bruce B. Peckham
In a one-parameter study of a noninvertible family of maps of the plane arising in the context of a numerical integration scheme, Lorenz studied a sequence of transitions from an a…