A counting result on two-dimension with error terms

DOI10.1080/17476930701228626zbMath1124.37026OpenAlexW2053045393MaRDI QIDQ5297075

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Publication date: 18 July 2007

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930701228626

zbMATH Keywords

periodic orbitsFourier transformsthermodynamic formalismhyperbolic dynamic systemsasymptotic estimates of closed orbitsquadratic polynomials on the complex planeRuelle-Perron-Frobenius operators

Mathematics Subject Classification ID

Periodic orbits of vector fields and flows (37C27) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (1)

Simultaneous action of finitely many interval maps: some dynamical and statistical properties

Cites Work

• An extension of the theory of Fredholm determinants
• Central limit asymptotics for shifts of finite type
• Homology properties of Y-systems
• Markov partitions for Anosov flows on \(n\)-dimensional manifolds
• Error terms for closed orbits of hyperbolic flows
• The dynamics of rational transforms: the topological picture
• Rates of Recurrence for Z ^q and R ^q Extensions of Subshifts of Finite Type
• Symbolic Dynamics for Hyperbolic Flows
• Ergodic theory of equilibrium states for rational maps

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