N. Haydn, Meromorphic extension of the zeta function for Axiom A flows, 10 (1990), 347-360. Home/Search Document Not in Database Summary Related Articles Check |
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On Systems With Finite Ergodic Degree - Isola (2000) (1 citation) (Correct)
....to some complex Dipartimento di Matematica e Fisica dell Universit a di Camerino and INFM, via Madonna delle Carceri, 62032 Camerino, Italy. e mail: isola campus.unicam.it . 1 domain where their poles are in correspondence with the isolated eigenvalues of the transfer operator (see [Ba2] [Hay], Pol1] Ru3] If var n V decays at a sub exponential rate one does not expect a spectral gap any more and the determination of the rate of mixing becomes a challenging problem. In [Pol2] this problem has been adressed for potentials of summable variation, for which it is known [Wal1] that ....
....we have the following relation for the grand partition function Xi (z) Xi (z) X oe2 Sigma S oe=oe exp Gamma1 X j=0 W z (T j oe) X j (M z 1 j ) oe (j) 9.130) The assertion now follows by putting together (9.130) Theorem 3. 1 and a straightforward extension of ([Hay], Theorem 4) to the present situation . From Proposition 4.3 and Proposition 9.7 we then have the following, Corollary 9.4 1. 1=i( w) is holomorphic in the disk of radius 1= Its zeroes in this disk, counted with multiplicity, are the inverses of the eigenvalues of M : F F in the ....
N T A Haydn, Meromorphic extension of the zeta function for Axiom A flows, Erg. Th. Dyn. Sys. 10 (1990), 347-360.
Decay of Correlations - Baladi (1999) (Correct)
.... diffeomorphisms) and Ruelle (Axiom A attractors) If f is topologically mixing (one may reduce to this case via the Smale spectral decomposition) then (f; is mixing and correlations decay exponentially fast for Holder observables (see e.g. Bow] Ru3] Pollicott [Po1] Ruelle [Ru4] and Haydn [Ha1, Ha2] obtained important results relating the correlation function and the zeta function. The above results were first obtained using Markov partitions and symbolic dynamics to reduce to a transfer operator defined from a subshift of finite type and a Holder weight. Different proofs using Birkhoff ....
N.T.A. Haydn, Meromorphic extension of the zeta function for Axiom A flows, Ergodic Theory Dynam. Systems 10 (1990), 347--360.
Dynamical Zeta Functions - Pollicott (Correct)
....real valued function g : R. The main result on the domain of i f (g; z) is the following Proposition. The zeta function i f (g; z) has a non zero meromorphic extension to a disk jzj Gamma1 e GammaP (g) for some 0 1, with a simple pole at z = e GammaP (g) Ru3] PP2] [Ha] analytic and non zero z f (g,z) z (g,z) f meromorphic and non zero e e q 1 P(g) P(g) Figure. Tha analytic and meromorphic domains of i f (s; g) Remark. By meromorphic, we mean analytic except for possibly finitely many poles of finite order. We shall return to the idea of the proof when we ....
N. Haydn, Meromorphic extension of the zeta function for Axiom A flows, Ergod. Th. and Dyanm. Sys. 10 (190), 347-360. DYNAMICAL ZETA FUNCTIONS 19
A Formula For The Essential Spectral Radius Of Ruelle's.. - Gundlach, Latushkin (Correct)
.... decay of correlations for all but finitely many linearly independent test functions from C r;ff , see [21] for the literature and recent advances on this topic; 2) the reciprocal to r ess (L; C r;ff ) gives the radius of meromorphy for the weighted i function associated with the system, see [3, 15, 23, 26]. 1991 Mathematics Subject Classification. Primary 58F03, 58F15; Secondary 60J10, 54H20. Key words and phrases. Transfer operator, random dynamical systems, multiplicative ergodic theorem, thermodynamical formalism, wavelets, essential spectral radius. YL was supported by the NSF grant ....
Haydn, N.: Meromorphic extension of the zeta function for Axiom A flows. Ergod. Th. Dynam. Sys. 10, 347--360 (1990).
Error Terms for Closed Orbits of Hyperbolic Flows - Pollicott, Sharp (Correct)
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N. Haydn, Meromorphic extension of the zeta function for Axiom A flows, 10 (1990), 347-360.
Error Terms for Closed Orbits of Hyperbolic Flows - Pollicott, Sharp (Correct)
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N. Haydn, Meromorphic extension of the zeta function for Axiom A flows, 10 (1990), 347-360.
Sharp Estimates in Ruelle Theorems for Matrix Transfer.. - Campbell, Latushkin (1997) (2 citations) (Correct)
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Haydn, N.: Meromorphic extension of the zeta function for Axiom A flows. Ergod. Th. Dynam. Sys. 10, 347--360 (1990).
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