Abstract
Our theme is the following: when it is known that a certain property holds for almost every point in a manifold, we want to know whether the property holds for almost every point in a submanifold or fractal subset. Such results were proved by Kleinbock and Margulis for Diophantine approximation via dynamics on homogeneous spaces, and by Masur and Veech for interval exchanges via dynamics on quadratic differential spaces. We survey some recent work along these lines, and also prove some new results, including a generalization of the convergence case of Khinchin’s theorem to a class of fractals in ℝd.
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Weiss, B. (2002). Dynamics on Parameter Spaces: Submanifold and Fractal Subset Questions. In: Burger, M., Iozzi, A. (eds) Rigidity in Dynamics and Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04743-9_23
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DOI: https://doi.org/10.1007/978-3-662-04743-9_23
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