On the topological pressure of the saturated set with non-uniform structure

We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1605.07283; text overlap with arXiv:1304.5497 by other author