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

DOI10.1017/S0143385700008087zbMath0818.58013MaRDI QIDQ4316568

Viviane Baladi, David Pierre Ruelle

Publication date: 11 December 1994

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

interval mapkneading invariantweighted zeta functionMilnor-Thurston

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Low-dimensional dynamical systems (37E99)

Related Items

Kneading operators, sharp determinants, and weighted Lefschetz zeta functions in higher dimensions ⋮ Dynamical zeta functions and kneading determinants: A linear algebra point of view ⋮ Functional equation for dynamical zeta functions of Milnor-Thurston type ⋮ Dynamical Zeta Functions for Maps of the Interval ⋮ Sharp determinants ⋮ Kneading with weights ⋮ On the effect of pruning on the singularity structure of zeta functions ⋮ A polynomial bound for the lap number ⋮ The quest for the ultimate anisotropic Banach space ⋮ Computation of symbolic dynamics for one-dimensional maps ⋮ Pseudo random sequences generated by piecewise linear maps from the view point of dynamical system ⋮ On fair entropy of the tent family ⋮ PIECEWISE LINEAR MODEL FOR TREE MAPS ⋮ Spectral invariants of periodic nonautonomous discrete dynamical systems ⋮ The Milnor-Thurston determinant and the Ruelle transfer operator

Cites Work

• What you need to know to knead
• Zeta functions and transfer operators for piecewise monotone transformations
• The Ruelle-Araki transfer operator in classical statistical mechanics
• The structure of Lorenz attractors
• Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps