Translator Disclaimer
1 December 2019 Beyond expansion, III: Reciprocal geodesics
Jean Bourgain, Alex Kontorovich
Duke Math. J. 168(18): 3413-3435 (1 December 2019). DOI: 10.1215/00127094-2019-0056

Abstract

We prove the existence of infinitely many low-lying and fundamental closed geodesics on the modular surface which are reciprocal, that is, invariant under time reversal. The method combines ideas from parts I and II of this series, namely, the dispersion method in bilinear forms, as applied to thin semigroups coming from restricted continued fractions.

Citation

Download Citation

Jean Bourgain. Alex Kontorovich. "Beyond expansion, III: Reciprocal geodesics." Duke Math. J. 168 (18) 3413 - 3435, 1 December 2019. https://doi.org/10.1215/00127094-2019-0056

Information

Received: 9 August 2018; Revised: 8 May 2019; Published: 1 December 2019
First available in Project Euclid: 15 November 2019

zbMATH: 07174391
MathSciNet: MR4034890
Digital Object Identifier: 10.1215/00127094-2019-0056

Subjects:
Primary: 11J70
Secondary: 11N36 , 37A45

Keywords: affine sieve , reciprocal geodesics , Thermodynamic formalism

Rights: Copyright © 2019 Duke University Press

JOURNAL ARTICLE
23 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.168 • No. 18 • 1 December 2019
Back to Top