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Abstract: this paper we shall consider error terms in estimates for the number of closed orbits for a large class of C flows # t : M M , restricted to a hyperbolic set #. Let #(T ) be the number of closed orbits of least period at most T > 0. It is well known that h = lim T#+# log #(T ), where h > 0 denotes the topological entropy of the flow. It was shown by Parry and the first author in [7] that if # is a weak-mixing Axiom A flow (restricted to a non-trivial basic set) then , as T +#... (Update)
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BibTeX entry: (Update)
@misc{ pollicott-error,
author = "Mark Pollicott and Richard Sharp",
title = "Error Terms for Closed Orbits of Hyperbolic Flows",
url = "citeseer.ist.psu.edu/603356.html" }
Citations (may not include all citations):144 Thermodynamic Formalism (context) - Ruelle - 1978
61 Oxford University Press (context) - Titchmarsh, of - 1939
32 Symbolic dynamics for hyperbolic flows (context) - Bowen - 1973
29 An extension of the theory of Fredholm determinants (context) - Ruelle - 1990
13 Prime numbers (context) - Ellison - 1975
12 The distribution of prime numbers (context) - Ingham - 1932
12 Markov partitions for Anosov flows on n-dimensional manifold.. (context) - Ratner - 1973
11 the rate of mixing for Axiom A flows (context) - Pollicott - 1985
9 On some applications of ergodic theory to the study of manif.. (context) - Margulis - 1969
9 An analogue of the prime number theorem for closed orbits of.. (context) - Parry, Pollicott - 1983
7 Prevalence of rapid mixing in hyperbolic flows (context) - Dolgopyat - 1998
7 Meromorphic extension of the zeta function for Axiom A flows (context) - Haydn - 1990
4 Zeta functions and the closed orbit structure of hyperbolic .. (context) - Parry, Pollicott - 1990
4 Error terms for growth functions on negatively curved surfac.. (context) - Pollicott, Sharp - 1998
3 375-387 (context) - Walters, theorem et al. - 1975
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