Zeta functions for gradients of closed 1-forms

DOI10.1016/j.topol.2004.04.005zbMath1053.37010OpenAlexW2079292103MaRDI QIDQ1886714

Dirk Schuetz

Publication date: 19 November 2004

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2004.04.005

zbMATH Keywords

zeta functionclosed 1-formsNovikov complexclosed orbit structuregradient-like vector fields

Mathematics Subject Classification ID

Periodic orbits of vector fields and flows (37C27) Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems (37B35) Critical points and critical submanifolds in differential topology (57R70) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Cites Work

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• Zeros of closed 1-forms, homoclinic orbits and Lusternik-Schnirelman theory.
• Homological identities for closed orbits
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• Trace and torsion in the theory of flows
• On the Lusternik-Schnirelman theory of a real cohomology class
• One-parameter fixed-point theory and gradient flows of closed 1-forms
• On the Novikov complex for rational Morse forms
• The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelman category
• Reidemeister torsion in generalized Morse theory
• Parameterized Lefschetz-Nielsen Fixed Point Theory and Hochschild Homology Traces
• Gradient flows of closed 1-forms and their closed orbits
• Simple homotopy type of the Novikov complex and the Lefschetz ζ-function of a gradient flow
• An Index of Fixed Point Type for Periodic Orbits
• Closed orbits of gradient flows and logarithms of non-abelian Witt vectors
• Controlled connectivity of closed \(1\)-forms

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