@article{BSMF_1976__104__195_0, author = {Mayer, Dieter H.}, title = {On a $\zeta $ function related to the continued fraction transformation}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {195--203}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {104}, year = {1976}, doi = {10.24033/bsmf.1825}, mrnumber = {54 #6210}, zbl = {0328.58011}, language = {en}, url = {https://www.numdam.org/articles/10.24033/bsmf.1825/} }
TY - JOUR AU - Mayer, Dieter H. TI - On a $\zeta $ function related to the continued fraction transformation JO - Bulletin de la Société Mathématique de France PY - 1976 SP - 195 EP - 203 VL - 104 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.1825/ DO - 10.24033/bsmf.1825 LA - en ID - BSMF_1976__104__195_0 ER -
%0 Journal Article %A Mayer, Dieter H. %T On a $\zeta $ function related to the continued fraction transformation %J Bulletin de la Société Mathématique de France %D 1976 %P 195-203 %V 104 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.1825/ %R 10.24033/bsmf.1825 %G en %F BSMF_1976__104__195_0
Mayer, Dieter H. On a $\zeta $ function related to the continued fraction transformation. Bulletin de la Société Mathématique de France, Tome 104 (1976), pp. 195-203. doi : 10.24033/bsmf.1825. https://www.numdam.org/articles/10.24033/bsmf.1825/
[1] On periodic points, Annals of Math., Series 2, t. 81, 1965, p. 82-99. | Zbl
and . -[2] Ergodic theory and information. - New York, J. Wiley, 1965 (Wiley Series in Probability and mathematical Statistics). | MR | Zbl
. -[3] Produits tensoriels topologiques et espaces nucléaires. - Providence, American mathematical Society, 1955 (Memoirs of the American mathematical Society, 16). | MR | Zbl
. -[4] The spectra of composition operators on HP, J. functional Analysis, t. 18, 1975, p. 132-150. | MR | Zbl
. -[5] Generalized Ά functions for axiom A basic sets, Bull. Amer. math. Soc., t. 82, 1976, p. 153-156. | MR | Zbl
. -[6] Ά functions for expanding maps and Anosov flows, Bures-sur-Yvette, Institut des Hautes Études Scientifiques (Preprint, to appear in Invent. math.). | Zbl
. -[7] Produits tensoriels topologiques d'espaces vectoriels topologiques. Espaces vectoriels topologiques nucléaires. Applications, 1re année, 1953/1954. - Paris, Secrétariat mathématique 1954. | Zbl
. -[8] Private communication (non published).
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- On Khintchine exponents and Lyapunov exponents of continued fractions, Ergodic Theory and Dynamical Systems, Volume 29 (2009) no. 1, p. 73 | DOI:10.1017/s0143385708000138
- On the uniqueness of Gibbs states in some dynamical systems, Journal of Mathematical Sciences, Volume 161 (2009) no. 2, p. 250 | DOI:10.1007/s10958-009-9550-8
- On the Ruelle eigenvalue sequence, Ergodic Theory and Dynamical Systems, Volume 28 (2008) no. 06, p. 1701 | DOI:10.1017/s0143385708000059
- A dynamical approach to accelerating numerical integration with equidistributed points, Proceedings of the Steklov Institute of Mathematics, Volume 256 (2007) no. 1, p. 275 | DOI:10.1134/s0081543807010166
- Symbolic dynamics for the modular surface and beyond, Bulletin of the American Mathematical Society, Volume 44 (2006) no. 1, p. 87 | DOI:10.1090/s0273-0979-06-01115-3
- Dynamical Zeta Functions and Closed Orbits for Geodesic and Hyperbolic Flows, Frontiers in Number Theory, Physics, and Geometry I (2006), p. 379 | DOI:10.1007/978-3-540-31347-2_11
- On the spectrum of Farey and Gauss maps, Nonlinearity, Volume 15 (2002) no. 5, p. 1521 | DOI:10.1088/0951-7715/15/5/310
- Dynamical sources in information theory: Fundamental intervals and word prefixes, Algorithmica, Volume 29 (2001) no. 1-2, p. 262 | DOI:10.1007/bf02679622
- Continued fraction algorithms, functional operators, and structure constants, Theoretical Computer Science, Volume 194 (1998) no. 1-2, p. 1 | DOI:10.1016/s0304-3975(97)00123-0
- Dynamical Zeta Functions, Real and Complex Dynamical Systems (1995), p. 1 | DOI:10.1007/978-94-015-8439-5_1
- An analysis of the Gaussian algorithm for lattice reduction, Algorithmic Number Theory, Volume 877 (1994), p. 144 | DOI:10.1007/3-540-58691-1_52
- On the spectra of randomly perturbed expanding maps, Communications in Mathematical Physics, Volume 156 (1993) no. 2, p. 355 | DOI:10.1007/bf02098487
- Dynamics of the continued fraction map and the spectral theory of SL (2, Z), Inventiones Mathematicae, Volume 114 (1993) no. 1, p. 207 | DOI:10.1007/bf01232667
- Circle Maps: Irrationally Winding, From Number Theory to Physics (1992), p. 631 | DOI:10.1007/978-3-662-02838-4_13
- Dynamical Zeta Functions: Where Do They Come from and What Are They Good for ?, Mathematical Physics X (1992), p. 43 | DOI:10.1007/978-3-642-77303-7_4
- On the thermodynamic formalism for the Gauss map, Communications in Mathematical Physics, Volume 139 (1991) no. 2, p. 311 | DOI:10.1007/bf02102958
- A note on the Artuso-Aurell-Cvitanovic approach to the Feigenbaum tangent operator, Journal of Statistical Physics, Volume 62 (1991) no. 1-2, p. 257 | DOI:10.1007/bf01020869
- On the thermodynamic formalism for the gauss map, Communications in Mathematical Physics, Volume 130 (1990) no. 2, p. 311 | DOI:10.1007/bf02473355
- Recycling of strange sets: II. Applications, Nonlinearity, Volume 3 (1990) no. 2, p. 361 | DOI:10.1088/0951-7715/3/2/006
- An extension of the theory of Fredholm determinants, Publications mathématiques de l'IHÉS, Volume 72 (1990) no. 1, p. 175 | DOI:10.1007/bf02699133
- On the relaxation time of Gauss' continued-fraction map. II. The Banach space approach (transfer operator method), Journal of Statistical Physics, Volume 50 (1988) no. 1-2, p. 331 | DOI:10.1007/bf01022997
- On the location of poles of Ruelle's zeta function, Letters in Mathematical Physics, Volume 14 (1987) no. 2, p. 105 | DOI:10.1007/bf00420300
- Relaxation properties of the mixmaster universe, Physics Letters A, Volume 121 (1987) no. 8-9, p. 390 | DOI:10.1016/0375-9601(87)90483-x
- Asymptotic distribution of closed geodesics, Israel Journal of Mathematics, Volume 52 (1985) no. 3, p. 209 | DOI:10.1007/bf02786516
- Approach to equilibrium for locally expanding maps in ? k, Communications in Mathematical Physics, Volume 95 (1984) no. 1, p. 1 | DOI:10.1007/bf01215752
- On composition operators on Banach spaces of holomorphic functions, Journal of Functional Analysis, Volume 35 (1980) no. 2, p. 191 | DOI:10.1016/0022-1236(80)90004-x
- On the ζ-function of a one-dimensional classical system of hard-rods, Communications in Mathematical Physics, Volume 52 (1977) no. 2, p. 175 | DOI:10.1007/bf01625782
- Statistical mechanics of one-dimensional Ising and Potts models with exponential interactions, Physica A: Statistical Mechanics and its Applications, Volume 89 (1977) no. 1, p. 97 | DOI:10.1016/0378-4371(77)90142-x
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