VOL. 188 · NO. 1 | July 2018
Steven Frankel
Ann. of Math. (2) 188 (1), 1-48, (July 2018) DOI: 10.4007/annals.2018.188.1.1
KEYWORDS: quasigeodesic flows, Pseudo-Anosov flows, Closed orbits, periodic orbits, hyperbolic dynamics, hyperbolic manifolds, 57M60, 57M50, 37C27
Paul Balister, Béla Bollobás, Robert Morris
Ann. of Math. (2) 188 (1), 49-143, (July 2018) DOI: 10.4007/annals.2018.188.1.2
KEYWORDS: integer factorization, perfect square, random graph process, 11Y05, 60C05
Carlos Moreira
Ann. of Math. (2) 188 (1), 145-170, (July 2018) DOI: 10.4007/annals.2018.188.1.3
KEYWORDS: Markov and Lagrange spectra, continued fractions, fractal dimensions, regular Cantor sets, 11J06, 11J70, 28A78, 37D20
Assaf Naor, Robert Young
Ann. of Math. (2) 188 (1), 171-279, (July 2018) DOI: 10.4007/annals.2018.188.1.4
KEYWORDS: Heisenberg group, Isoperimetric inequalities, metric embeddings, Sparsest Cut Problem, approximation algorithms, semidefinite programming, metrics of negative type, 46B85, 20F65, 30L055, 68W25, 43A15
Alex Eskin, Simion Filip, Alex Wright
Ann. of Math. (2) 188 (1), 281-313, (July 2018) DOI: 10.4007/annals.2018.188.1.5
KEYWORDS: Teichmüller geodesic flow, Abelian differential, Kontsevich--Zorich cocycle, algebraic hull, 32G15, 7D40, 14D07, 37C85
Vadim Kaloshin, Alfonso Sorrentino
Ann. of Math. (2) 188 (1), 315-380, (July 2018) DOI: 10.4007/annals.2018.188.1.6
KEYWORDS: Birkhoff billiards, integrable billiards, integrable systems, elliptic function, complex singularities, action-angle coordinates, 37J35, 70H06, 37E40, 33E05, 35A20, 37D50
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