# Billiard Ordered Games and Books

@article{Dragovi2022BilliardOG, title={Billiard Ordered Games and Books}, author={Vladimir Dragovi{\'c} and Sean Gasiorek and Milena Radnovi{\'c}}, journal={Regular and Chaotic Dynamics}, year={2022} }

We consider billiard ordered games and, using a recently developed idea of elliptic billiard books, we construct the configuration space for them. Dynamical and topological properties of the systems obtained in that way are considered.

## References

SHOWING 1-10 OF 54 REFERENCES

### Bifurcations of Liouville tori in elliptical billiards

- Mathematics, Physics
- 2009

A detailed description of topology of integrable billiard systems is given. For elliptical billiards and geodesic billiards on ellipsoid, the corresponding Fomenko graphs are constructed.

### Pseudo-integrable billiards and double reflection nets

- Mathematics
- 2015

This is a survey of two recently emerged directions in the study of billiards inside pencils of quadrics: pseudo-integrable billiards in the plane and double reflection nets. Bibliography: 48 titles.

### Topology of the elliptical billiard with the Hooke's potential

- Physics, Mathematics
- 2015

Using Fomenko graphs, we present a topological description of the elliptical billiard with Hooke's potential.

### Geometry and billiards

- Mathematics, Physics
- 2005

Motivation: Mechanics and optics Billiard in the circle and the square Billiard ball map and integral geometry Billiards inside conics and quadrics Existence and non-existence of caustics Periodic…

### Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems

- MathematicsSbornik: Mathematics
- 2018

We introduce a new class of billiards—billiard books, which are integrable Hamiltonian systems. It turns out that for any nondegenerate three-dimensional bifurcation (3-atom), a billiard book can be…

### CORRIGENDUM: Cayley-type conditions for billiards within k quadrics in Bbb Rd

- Mathematics
- 2005

In section 4 of this paper, the authors misstated theorems 3 and 4. Please see PDF for corrected theorems.

### The Liouville Foliation of the Billiard Book Modelling the Goryachev-Chaplygin Case

- Mathematics
- 2020

The Fomenko-Zieschang invariant of an interesting case of an integrable billiard book is calculated and it is shown that such a book models dynamics of the Goryachev-Chaplygin integrable case on a…

### Integrable billiards and quadrics

- Mathematics
- 2010

Billiards inside quadrics are considered as integrable dynamical systems with a rich geometric structure. The two-way interaction between the dynamics of billiards and the geometry of pencils of…

### Minkowski plane, confocal conics, and billiards

- Mathematics, Physics
- 2013

Geometry of confocal conics in the Minkowski plane and related billiard
dynamics are studied in details. Periodic trajectories are described and
several new examples are presented. Topological…

### Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity

- Psychology
- 1990

CONTENTS § 1. Introduction § 2. Realizability theorem § 3. Tagged skeletons § 4. Coding integrable Hamiltonian systems References