Hausdorff Dimension of Order Preserving Sets
Communications in Mathematical Physics
Letg aC 2 generic bimodal map of the circle. We prove that the closure of the union of the order preserving recurrent sets with irrational rotation number has Hausdorff dimension zero. This set contains order preserving periodic orbits with each rotation numberp/q in the rotation interval ofg.
Copyright (1990) Springer
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Veerman, J. J. P. (1990). Hausdorff dimension of order preserving sets. Communications in mathematical physics, 127(2), 313-317.