Density of periodic measures and large deviation principle for generalized (α, β)-transformations
Abstract
We introduce generalized (α,β)-transformations, which include all (α,β) and generalized β-transformations, and prove that all transitive generalized (α,β)-transformations satisfy the level-2 large deviation principle with a unique measure of maximal entropy. A crucial step in our proof is to establish density of periodic measures in the set of ergodic measures.
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