Density of periodic measures and large deviation principle for generalized $(α, β)$-transformations

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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