Dynamical systems of the billiard type are of fundamental importance for the description of numerous phenomena observed in many different fields of research, including statistical mechanics, Hamiltonian dynamics, nonlinear physics, and many others. This Focus Issue presents the recent progress in this area with contributions from the mathematical as well as physical stand point.

1.
N. S.
Krylov
,
Works on the Foundations of Statistical Physics
(
Princeton University Press
,
Princeton, NJ
,
1979
).
2.
G. A.
Hedlund
, “
The dynamics of geodesic flows
,”
Bull. Am. Math. Soc.
45
,
241
(
1939
).
3.
E.
Hopf
, “
Statistik der geodetischen Linien in Mannigfaltigkeiten negativer Kriimmung
,”
Ber. Verh. Saechs. Akad,. Wiss. Leipzig
91
,
261
(
1939
).
4.
Ya. G.
Sinai
, “
Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards
,”
Russ. Math. Surveys Dokl. Acad. Sci. USSR
25
,
137
(
1970
).
5.
L. A.
Bunimovich
, “
On the ergodic properties of billiards close to dispersing ones
,”
Dokl. Acad. Sci. USSR
211
,
1024
(
1973
);
L. A.
Bunimovich
, “
On ergodic properties of some billiards
,”
Funct. Anal. Appl.
8
,
254
(
1974
).
6.
V.
Rom-Kedar
and
D.
Turaev
, “
Billiards: A singular perturbation limit of smooth Hamiltonian flows
,”
Chaos
22
,
026102
(
2012
).
7.
L. A.
Bunimovich
and
L. V.
Vela-Arevalo
, “
Many faces of stickiness in Hamiltonian systems
,”
Chaos
22
,
026103
(
2012
).
8.
P.
Bálint
,
G.
Borbély
, and
A. N.
Varga
, “
Statistical properties of the system of two falling balls
,”
Chaos
22
,
026104
(
2012
).
9.
N.
Chernov
,
A.
Korepanov
, and
N.
Simanyi
, “
Stable regimes for hard disks in a channel with twisting walls
,”
Chaos
22
,
026105
(
2012
).
10.
G.
Del Magno
,
J. L.
Dias
,
P.
Duarte
,
J. P.
Gaivão
, and
D.
Pinheiro
, “
Chaos in the square billiard with a modfied reflection law
,”
Chaos
22
,
026106
(
2012
).
11.
A.
Arroyo
,
R.
Markarian
, and
D. P.
Sanders
, “
Structure and evolution of strange attractors in non-elastic triangular billiards
,”
Chaos
22
,
026107
(
2012
).
12.
G.
Gallavotti
,
G.
Gentile
, and
A.
Giuliani
, “
Resonances within chaos
,”
Chaos
22
,
026108
(
2012
).
13.
S.
Pinto-de-Carvalho
and
R.
Ramírez-Ros
, “
Billiards with a given number of (k, n)-orbits
,”
Chaos
22
,
026109
(
2012
).
14.
P. S.
Casas
and
R.
Ramírez-Ros
, “
Classification of symmetric periodic trajectories in ellipsoidal billiards
,”
Chaos
22
,
026110
(
2012
).
15.
H. A.
Oliveira
,
G. A.
Emidio
, and
M. W.
Beims
, “
Three unequal masses on a ring and soft triangular billiards
,”
Chaos
22
,
026111
(
2012
).
16.
M. S.
Custódio
,
C.
Manchein
, and
M. W.
Beims
, “
Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems
,”
Chaos
22
,
026112
(
2012
).
17.
C. P.
Dettmann
and
O.
Georgiou
, “
Quantifying intermittency in the open drivebelt billiard
,”
Chaos
22
,
026113
(
2012
).
18.
E. G.
Altmann
,
J. C.
Leitão
, and
J. V.
Lopes
, “
Effect of noise in open chaotic billiards
,”
Chaos
22
,
026114
(
2012
).
19.
P.
Nándori
and
D.
Szász
, “
Lorentz process with shrinking holes in a wall
,”
Chaos
22
,
026115
(
2012
).
20.
E.
Gutkin
, “
Billiards Dynamics: An updated survey with the emphasis on open problems
,”
Chaos
22
,
026116
(
2012
).
21.
P.
Gaspard
and
T.
Gilbert
, “
A two-stage approach to relaxation in billiard systems of locally conned hard spheres
,”
Chaos
22
,
026117
(
2012
).
22.
S.
Roy
and
A.
Pikovsky
, “
Spreading of energy in the Ding-Dong model
,”
Chaos
22
,
026118
(
2012
).
23.
A. P.
Itin
and
A. I.
Neishtadt
, “
Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances
,”
Chaos
22
,
026119
(
2012
).
24.
A. K.
Karlis
,
F. K.
Diakonos
, and
V.
Constantoudis
, “
A consistent approach for the treatment of Fermi acceleration in time-dependent billiards
,”
Chaos
22
,
026120
(
2012
).
25.
A. B.
Ryabov
and
A.
Loskutov
, “
The role of dissipation in time-dependent non-integrable focusing billiards
,”
Chaos
22
,
026121
(
2012
).
26.
A. L. P.
Livorati
,
I. L.
Caldas
, and
E. D.
Leonel
, “
Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard
,”
Chaos
22
,
026122
(
2012
).
27.
D. F. M.
Oliveira
and
E. D.
Leonel
, “
In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas
,”
Chaos
22
,
026123
(
2012
).
28.
J.
De-Simoi
and
D.
Dolgopyat
, “
Dynamics of some piecewise smooth Fermi-Ulam models
,”
Chaos
22
,
026124
(
2012
).
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