Yingjie Zhang
Abstract
We study the Hausdorff dimension of invariant sets for expanding maps and that of hyperbolic sets on unstable manifolds. Upper bounds for the Hausdorff dimension are given in terms of topological pressure, or topological entropy and Lyapunov exponents.
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We study the Hausdorff dimension of invariant sets for expanding maps and that of hyperbolic sets on unstable manifolds. Upper bounds for the Hausdorff dimension are given in terms of topological pressure, or topological entropy and Lyapunov exponents.
Key concepts: Hausdorff dimension, Mathematics, Topological entropy, Lyapunov exponent, Invariant (physics), Hausdorff space, Minkowski–Bouligand dimension, Pure mathematics