# Dynamics Done with Your Bare Hands: Lecture Notes by Diana Davis, Bryce Weaver, Roland K. W. Roeder, and Pablo Lessa

Share this page *Edited by *
*Françoise Dal’Bo; François Ledrappier; Amie Wilkinson*

A publication of the European Mathematical Society

This book arose from four lectures given at the Undergraduate Summer
School of the Thematic Program Dynamics and Boundaries, held at the
University of Notre Dame. It is intended to introduce (under)graduate
students to the field of dynamical systems by emphasizing elementary
examples, exercises, and bare hands constructions.

The lecture by Diana Davis is devoted to billiard flows on
polygons, a simple-sounding class of continuous time dynamical system
for which many problems remain open. Bryce Weaver focuses on the
dynamics of a \(2\times 2\) matrix acting on the flat torus. This example
introduced by Vladimir Arnold illustrates the wide class of uniformly
hyperbolic dynamical systems, including the geodesic flow for
negatively curved, compact manifolds. Roland Roeder considers a
dynamical system on the complex plane governed by a quadratic map with
a complex parameter. These maps exhibit complicated dynamics related
to the Mandelbrot set defined as the set of parameters for which the
orbit remains bounded. Pablo Lessa deals with a type of
non-deterministic dynamical system: a simple walk on an infinite
graph, obtained by starting at a vertex and choosing a random neighbor
at each step. The central question concerns the recurrence
property. When the graph is a Cayley graph of a group, the behavior of
the walk is deeply related to algebraic properties of the
group.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Reviews & Endorsements

Each of the chapters has oodles of cool ideas that could interest students equipped with enough enthusiasm and a sufficient background in analysis, topology and algebra...there is a lot of excellent material here that could offer useful starting points for student projects.

-- Bill Satzer, Mathematical Reviews