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A typical orbit for: $z\mapsto\beta z \mod \mathbb Z^2$ for $|\beta|>1$.

## What is this Wiki for?

This is a place for (references to) uses of and results about dynamical systems (including group actions) defined by piecewise affine transformations.

We are interested in their mathematical theory including conjectures as well as numerical experiments and applications of these systems.

## Who is this Wiki for?

It was created by a group of French mathematicians but anyone working on related subjects is invited to join. In order to avoid spam you must register before editing pages or posting comments. You can do it here. If you are a member you can also send invitation from that page.

## What can you do?

Thank you for adding information about these fascinating dynamical systems. We hope to gather short introductions and foremost references and links to the analysis and applications of piecewise affine dynamics.

## Organization of the Wiki

Please note that this wiki uses **tags** to structure its pages. As of now the following tags should be used (feel free to add others if necessary, but please add them also at the end of this list):

*ergodic-theory; topological-dynamics; topological-entropy; KS-entropy; non-uniform-hyperbolicity; symbolic-dynamics; periodic-points; symbolic-extension-entropy; parameters; continuity-of-the-entropy; maximal-entropy-measures; absolutely-continuous-invariant-measures; piecewise-expanding; piecewise-hyperbolic; piecewise-isometric; continuous; homeomorphism; surface; higher-dimension; lozi; simulations; rigorous-estimates; theoretical-computer-science*

**Note.** Each tag is one word.

The wiki is also organized hierarchically: each page is given a **parent** (using the "parent" button which is accessed by clicking on "options" at the bottom of the page). The "Table of Content" buttom in the top bar displays this structure.