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• W2950992370 abstract "Given a non-conformal repeller $Lambda$ of a $C^{1+gamma}$ map, we study the Hausdorff dimension of the repeller and continuity of the sub-additive topological pressure for the sub-additive singular valued potentials. Such a potential always possesses an equilibrium state. We then use a substantially modified version of Katok's approximating argument, to construct a compact invariant set on which the corresponding dynamical quantities (such as Lyapunov exponents and metric entropy) are close to that of the equilibrium measure. This allows us to establish continuity of the sub-additive topological pressure and obtain a sharp lower bound of the Hausdorff dimension of the repeller. The latter is given by the zero of the super-additive topological pressure" @default.
• W2950992370 created "2019-06-27" @default.
• W2950992370 creator A5011627395 @default.
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• W2950992370 date "2019-06-17" @default.
• W2950992370 modified "2023-09-26" @default.
• W2950992370 title "Dimension Estimates for Non-conformal Repellers and Continuity of Sub-additive Topological Pressure" @default.
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• W2950992370 doi "https://doi.org/10.48550/arxiv.1906.07323" @default.
• W2950992370 hasPublicationYear "2019" @default.
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