TY - JOUR
T1 - Beyond expansion, III
T2 - Reciprocal geodesics
AU - Bourgain, Jean
AU - Kontorovich, Alex
N1 - Funding Information:
Bourgain’s work was partially supported by National Science Foundation (NSF) grant DMS-1301619. Kontorovich’s work was partially supported by NSF CAREER grants DMS-1254788 and DMS-1455705, NSF FRG grant DMS-1463940, an Alfred P. Sloan Research Fellowship, and a grant from the United States–Israel Binational Foundation.
Publisher Copyright:
© 2019 Duke University Press. All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
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U2 - 10.1215/00127094-2019-0056
DO - 10.1215/00127094-2019-0056
M3 - Article
AN - SCOPUS:85075932839
SN - 0012-7094
VL - 168
SP - 3413
EP - 3435
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 18
ER -