Work

New classes of quasigeodesic Anosov flows in $3$ -manifolds

Year: 2024

Type: article

Abstract: Quasigeodesic behavior of flow lines is a very useful property in the study of Anosov flows. Not every Anosov flow in dimension three is quasigeodesic. In fact, until recently, up to orbit equivalence, the only previously known examples of quasigeodesic Anosov flows were suspension flows. In a recent article, the second author proved that an Anosov flow on a hyperbolic 3-manifold is quasigeodesic if and only if it is non- $\mathbb {R}$ -covered, and this result completes the classification of quasigeodesic Anosov flows on hyperbolic 3-manifolds. In this article, we prove that a new class of examples of Anosov flows are quasigeodesic. These are the first examples of quasigeodesic Anosov flows on 3-manifolds that are neither Seifert, nor solvable, nor hyperbolic. In general, it is very hard to show that a given flow is quasigeodesic and, in this article, we provide a new method to prove that an Anosov flow is quasigeodesic.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2024.89

Authors: ANINDYA CHANDA, SÉRGIO R. FENLEY

Institutions: Tata Institute of Fundamental Research, Florida State University, Institute for Advanced Study

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funders: National Science Foundation, Simons Foundation