Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
نویسنده
چکیده
0. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part I. Renewal theorems in symbolic dynamics . . . . . . . . . . . . 1. Background: Shifts, suspension flows, thermodynamic formalism . 2. 3. 4. 5. 6. 7. 1 5 5 Renewal measures and renewal theorems . . . . . . . . . . . . . . 7 A modification for finite sequences . . . . . . . . . . . . . . . . . 10 Equidistribution theorems . . . . . . . . . . . . . . . . . . . . . . 13 Periodic orbits of suspension flows . . . . . . . . . . . . . . . . . 17 Proof of Theorem 4 . . . . . . . . . . . . . . . . . . . . . . . . . 20 Perturbation theory for Perron-Frobenius operators . . . . . . . . 23 8. Fourier analysis of the renewal equation . . . . . . . . . . . . . . 26 Part II. Applications to discrete groups . . . . . . . . . . . . . . . . . 32 9. Symbolic dynamics for Schottky groups . . . . . . . . . . . . . . 32 10. Symbolic dynamics for Fuchsian groups . . . . . . . . . . . . . . 34 11. The geodesic flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 12. Distribution of noneuclidean lattice points and fundamental polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 13. Packing and covering functions of the limit set . . . . . . . . . . . 43 14. Random walk and Hausdorff measure . . . . . . . . . . . . . . . . 53 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
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