Subshifts of finite type in linked twist mappings

Abstract

For each pair of nonzero integers j, k, we define a homeomorphism f j , k {f_{j,k}} of the two-disk minus three holes. We show that there exists a compact, invariant, hyperbolic set for each f j , k {f_{j,k}} on which f j , k {f_{j,k}} is conjugate to a subshift of finite type. This implies that the topological entropy of f j , k {f_{j,k}} is bounded below by 4 | j | | k | − 2 | j | − 2 | k | 4|j||k| - 2|j| - 2|k| .