Geodesic
Comparison theorems for closed geodesics on negatively curved surfaces
Stephen Cantrell1 ; Mark Pollicott2
1University of Chicago, USA
2University of Warwick, Coventry, UK
Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 461-491

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DOI

In this note, we present new asymptotic estimates comparing the word length and geodesic length of closed geodesics on surfaces with (variable) negative sectional curvatures. In particular, we provide an averaged comparison of these two important quantities and obtain precise statistical results, including a central limit theorem and a local limit theorem. Further, as a corollary we also improve an asymptotic formula of Sharp and the second author (1998). Finally, we relate our results to a recent work of Gekhtman, Taylor, and Tiozzo (2019).
DOI : 10.4171/ggd/671
Classification : 37-XX, 20-XX
Mots-clés : Negatively curved surfaces, counting, statistical limit laws

Stephen Cantrell  1   ; Mark Pollicott  2

1 University of Chicago, USA
2 University of Warwick, Coventry, UK 
Stephen Cantrell; Mark Pollicott. Comparison theorems for closed geodesics on negatively curved surfaces. Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 461-491. doi: 10.4171/ggd/671
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     pages = {461--491},
     year = {2022},
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     number = {2},
     doi = {10.4171/ggd/671},
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}
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