Bowen asked whether the transformation on a subset of the plane known as linked twist mapping has any stochastic propcrties.' Devaney proved that linked twist mappings possess shift transformations as subsystems.* Easton introduced an analogous transformation that is simpler to study because it is piecewise linear.' We prove that, in some cases, the transformations have the K-property. In some other cases, we can only prove that they consist of K-components of positive measure. The same arguments arc applied to obtain explicit Co arbitrarily small perturbations of the twist mapping that consist of K-components of positive measure.
[1]
D. Saari,et al.
Stable and Random Motions in Dynamical Systems
,
1975
.
[2]
L. Bunimovich.
On the ergodic properties of nowhere dispersing billiards
,
1979
.
[3]
R. Devaney.
Subshifts of finite type in linked twist mappings
,
1978
.
[4]
Y. Sinai,et al.
Dynamical systems with elastic reflections
,
1970
.
[5]
Rufus Bowen,et al.
On axiom A diffeomorphisms
,
1975
.
[6]
Giovanni Gallavotti,et al.
Billiards and Bernoulli schemes
,
1974
.
[7]
R. Easton.
Chain transitivity and the domain of influence of an invariant set
,
1978
.