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Decay of correlations on Abelian covers of isometric extensions of volume-preserving Anosov flows

Mihajlo Cekić, Thibault Lefeuvre, Sebastián Muñoz-Thon

Abstract

We establish an asymptotic expansion in inverse powers of time of the correlation function of isometric extensions of volume-preserving Anosov flows on Abelian covers of closed manifolds.

Decay of correlations on Abelian covers of isometric extensions of volume-preserving Anosov flows

Abstract

We establish an asymptotic expansion in inverse powers of time of the correlation function of isometric extensions of volume-preserving Anosov flows on Abelian covers of closed manifolds.
Paper Structure (41 sections, 38 theorems, 251 equations)

This paper contains 41 sections, 38 theorems, 251 equations.

Table of Contents

  1. Introduction
  2. Decay of correlations for Anosov flows on Abelian covers
  3. Decay of correlations for isometric extensions of Anosov flows on Abelian covers
  4. Application to frame flows
  5. Related results
  6. Organization of the article
  7. Abelian covers and isometric extensions
  8. Abelian covers
  9. Floquet theory
  10. Topology of Abelian extensions
  11. Functional spaces on Abelian covers
  12. Dynamical connection
  13. Affine case
  14. Principal bundles
  15. Preliminaries on semiclassical analysis
  16. ...and 26 more sections

Key Result

Theorem 1.1

Let $\pi \colon M \to M_0$ be a $\mathbb{Z}^d$-cover corresponding to a surjective representation $\rho \colon \pi_1(M_0) \to \mathbb{Z}^d$ as in equation:zd-cover, and let $(\varphi_t)_{t \in \mathbb{R}}$ be a volume-preserving $\mathbb{Z}^d$-equivariant Anosov flow as above. If $d\alpha \neq 0$, t where the following estimates hold: for all $s > 0$, there exists a constant $C > 0$ such that whe

Theorems & Definitions (73)

  • Theorem 1.1: Decay of correlations on Abelian covers
  • Theorem 1.2
  • Corollary 1.3
  • Lemma 2.1
  • proof
  • Proposition 2.2
  • proof
  • Remark 2.3
  • Lemma 2.4
  • proof
  • ...and 63 more