The Hausdorff dimension of the set of points with nondense orbit under a hyperbolic dynamical system
β Scribed by Urbanski, M
- Book ID
- 121433869
- Publisher
- Institute of Physics
- Year
- 1991
- Tongue
- English
- Weight
- 495 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0951-7715
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π SIMILAR VOLUMES
Let m, n be positive integers and let : Z n Γ R be a non-negative function. Let W(m, n; ) be the set { X # R mn : " : n j=1 x ij q j " < (q), 1 i m, for infinitely many q # Z n = . The Hausdorff dimension of W(m, n; ) is obtained for arbitrary non-negative functions , with no monotonicity assumpti
In this paper we improve the construction of Goto (1993) to obtain the Main Theorem: Let n, m and k be arbitrary integers such that 0 < m < n -1 3 1 and m < k < min{2m, n -1). Then there exists a point set Xk,, in Euclidean n-space IR" such that (i) pdimX& = m and dimXk,, = k, (ii) pdim(X& n H) = m