S. Hayes

activity

20002020

collaborators

4 papers

math.DS2020

Quadratic Dynamics Over Hyperbolic Numbers

Sandra Hayes

Hyperbolic numbers are a variation of complex numbers, but their dynamics is quite different. The hyperbolic Mandelbrot set for quadratic functions over hyperbolic numbers is simpl…

math.DS2013

The Real Dynamics of Bieberbach's Example

Sandra Hayes, Axel Hundemer, Evan Milliken +1

Bieberbach constructed in 1933 domains in $C^{2}$ which were biholomorphic to $C^{2}$ but not dense. The existence of such domains was unexpected. The special domains Bie…

math.DS2013

Diffeomorphisms with stable manifolds as basin boundary

Sandra Hayes, Christian Wolf

In this paper we study the dynamics of a family of diffeomorphisms in $\bR^2$ defined by $F (x, y) = (g (x) + h (y), h (x)),$ where $g (x)$ is a unimodal $C^{2}$ -map which has the same dyna…

math.DG2000

Orbits of Lie Group Actions are Weakly Embedded

Domenico P. L. Castrigiano, Sandra A. Hayes

In this note we prove that whenever a Lie group $G$ acts on a manifold $X$ , then the orbit $G x$ through any point $x$ of $X$ is a weakly embedded submanifold of $X$ . The investigat…