ON THE RUELLE ZETA FUNCTION OF AN EXPANDING INTERVAL MAP

2007 ◽  
Author(s):  
JOÃO FERREIRA ALVES ◽  
J. L. FACHADA
Keyword(s):  
Zeta Function ◽  
Interval Map ◽  
Ruelle Zeta Function

scholarly journals Ruelle Zeta Function from Field Theory

2020 ◽  
Vol 21 (12) ◽  
pp. 3835-3867
Author(s):  
Charles Hadfield ◽  
Santosh Kandel ◽  
Michele Schiavina
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Zeta Function ◽  
Lagrangian Submanifolds ◽  
Analytic Torsion ◽  
Contact Manifolds ◽  
Gauge Fixing ◽  
Ruelle Zeta Function

Abstract We propose a field-theoretic interpretation of Ruelle zeta function and show how it can be seen as the partition function for BF theory when an unusual gauge-fixing condition on contact manifolds is imposed. This suggests an alternative rephrasing of a conjecture due to Fried on the equivalence between Ruelle zeta function and analytic torsion, in terms of homotopies of Lagrangian submanifolds.

scholarly journals On the distribution of zeros of a Ruelle zeta-function

1994 ◽  
Vol 159 (3) ◽  
pp. 433-441 ◽  
Author(s):  
A. Eremenko ◽  
G. Levin ◽  
M. Sodin
Keyword(s):  
Zeta Function ◽  
Distribution Of Zeros ◽  
Ruelle Zeta Function

An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps

1994 ◽  
Vol 14 (4) ◽  
pp. 621-632 ◽  
Author(s):  
V. Baladi ◽  
D. Ruelle
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Constant Weight ◽  
Piecewise Constant ◽  
Piecewise Monotone ◽  
Interval Maps ◽  
Interval Map ◽  
Piecewise Continuous

AbstractWe consider a piecewise continuous, piecewise monotone interval map and a piecewise constant weight. With these data we associate a weighted kneading matrix which generalizes the Milnor—Thurston matrix. We show that the determinant of this matrix is related to a natural weighted zeta function.

scholarly journals Growth and Zeros of the Zeta Function for Hyperbolic Rational Maps

2007 ◽  
Vol 59 (2) ◽  
pp. 311-331 ◽  
Author(s):  
Hans Christianson
Keyword(s):  
Dynamical System ◽  
Lower Bound ◽  
Zeta Function ◽  
Julia Set ◽  
Upper Bounds ◽  
Rational Maps ◽  
Rational Map ◽  
Numerical Work ◽  
Number Of Zeros ◽  
Ruelle Zeta Function

AbstractThis paper describes new results on the growth and zeros of the Ruelle zeta function for the Julia set of a hyperbolic rational map. It is shown that the zeta function is bounded by exp(CK|s|δ) in strips | Re s| ≤ K, where δ is the dimension of the Julia set. This leads to bounds on the number of zeros in strips (interpreted as the Pollicott–Ruelle resonances of this dynamical system). An upper bound on the number of zeros in polynomial regions {| Re s| ≤ | Im s|α} is given, followed by weaker lower bound estimates in strips {Re s > –C, | Ims| ≤ r}, and logarithmic neighbourhoods {| Re s| ≤ ρlog | Ims|}. Recent numerical work of Strain–Zworski suggests the upper bounds in strips are optimal.

scholarly journals Ruelle zeta function at zero for surfaces

2017 ◽  
Vol 210 (1) ◽  
pp. 211-229 ◽  
Author(s):  
Semyon Dyatlov ◽  
Maciej Zworski
Keyword(s):  
Zeta Function ◽  
Ruelle Zeta Function
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