American Institute of Mathematical Sciences

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  2019, 14: ⅴ-xxv. doi: 10.3934/jmd.2019v

Bill Veech's contributions to dynamical systems

Giovanni Forni 1, , Howard Masur 2, and  John Smillie 3,

1. 

Department of Mathematics, University of Maryland, College Park, MD 20742, USA
2. 

Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA
3. 

Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

Received  February 10, 2019 Published  February 2019

Citation: Giovanni Forni, Howard Masur, John Smillie. Bill Veech's contributions to dynamical systems. Journal of Modern Dynamics, 2019, 14: ⅴ-xxv. doi: 10.3934/jmd.2019v
References:
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show all references

References:
[1]

J. Auslander, G. Greschonig and A. Nagar, Reflections on equicontinuity, Proc. Amer. Math. Soc., 142 (2014), 3129-3137.  doi: 10.1090/S0002-9939-2014-12034-X.  Google Scholar

[2]

J. Athreya, A. Bufetov, A. Eskin and M. Mirzakhani, Lattice point asymptotics and volume growth on Teichmüller space, Duke Math. J., 161 (2012), 1055-1111.  doi: 10.1215/00127094-1548443.  Google Scholar

[3]

A. Avila and V. Delecroix, Weak mixing directions in non-arithmetic Veech surfaces, J. Amer. Math. Soc., 29 (2016), 1167-1208.  doi: 10.1090/jams/856.  Google Scholar

[4]

A. Avila and G. Forni, Weak mixing for interval exchange transformations, and translation flows, Ann. of Math., 165 (2007), 637-664.  doi: 10.4007/annals.2007.165.637.  Google Scholar

[5]

A. Avila and S. Gouëzel, Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow, Ann. of Math., 178 (2013), 385-442.  doi: 10.4007/annals.2013.178.2.1.  Google Scholar

[6]

A. Avila, S. Gouëzel and J.-C. Yoccoz, Exponential mixing for the Teichmüller flow, Publications Mathématiques de l'IHÉS, 104 (2006), 143-211.  doi: 10.1007/s10240-006-0001-5.  Google Scholar

[7]

A. Avila and M. Viana, Simplicity of Lyapunov spectra: Proof of the Zorich–Kontsevich conjecture, Acta Math., 198 (2007), 1-56.  doi: 10.1007/s11511-007-0012-1.  Google Scholar

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M. Bainbridge, J. Smillie and B. Weiss, Horocycle dynamics: new invariants and eigenform loci in the stratum H(1,1), preprint, arXiv: 1603.00808. Google Scholar

[9]

D. Bernazzani, Most interval exchanges have no roots, J. Mod. Dyn., 11 (2017), 249-262.  doi: 10.3934/jmd.2017011.  Google Scholar

[10]

C. Boldrighini, M. Keane and F. Marchetti, Billiards in polygons, Ann. Probab., 6 (1978), 532-540.  doi: 10.1214/aop/1176995475.  Google Scholar

[11]

M. Boshernitzan, A condition for minimal interval exchange maps to be uniquely ergodic, Duke Math. J., 52 (1985), 723-752.  doi: 10.1215/S0012-7094-85-05238-X.  Google Scholar

[12]

____, Rank two interval exchange transformations, Ergodic Theory and Dynamical Systems, 8(1988), 379–394. doi: 10.1017/S0143385700004521.  Google Scholar

[13]

I. I. Bouw and M. Möller, Teichmüller curves, triangle groups, and Lyapunov exponents, Ann. of Math., 172 (2010), 139-185.  doi: 10.4007/annals.2010.172.139.  Google Scholar

[14]

A. Bufetov, Logarithmic asymptotics for the number of periodic orbits of the Teichmüller flow on Veech's space of zippered rectangles, Mosc. Math. J., 9 (2009), 245-261.  doi: 10.17323/1609-4514-2009-9-2-245-261.  Google Scholar

[15]

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[16]

J. Chaika and A. Eskin, Self-Joinings for 3-IETs, preprint, arXiv: 1805.11167v2. Google Scholar

[17]

J. Chaika and R. Treviño, Logarithmic laws and unique ergodicity, J. Mod. Dyn., 11 (2017), 563-588.  doi: 10.3934/jmd.2017022.  Google Scholar

[18]

D. Chen, M. Möller and D. Zagier, Quasimodularity and large genus limits of Siegel-Veech constants, J. Amer. Math. Soc., 31 (2018), 1059-1163.  doi: 10.1090/jams/900.  Google Scholar

[19]

A. Danilenko and A. Solomko, Simple mixing actions with uncountably many prime factors, Colloq. Math., 139 (2015), 37-54.  doi: 10.4064/cm139-1-3.  Google Scholar

[20]

D. Dolgopyat, Livsic theory for compact group extensions of hyperbolic systems, Mosc. Math. J., 5 (2005), 55-67.  doi: 10.17323/1609-4514-2005-5-1-55-66.  Google Scholar

[21]

R. Ellis, The Veech structure theorem, Trans. of the Amer. Math. Soc., 186 (1973), 203-218.  doi: 10.1090/S0002-9947-1973-0350712-1.  Google Scholar

[22]

____, The Furstenberg structure theorem, Pacific Journal of Math., 76(1978), 345–349. doi: 10.2140/pjm.1978.76.345.  Google Scholar

[23]

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Figure 1.  Rauzy diagram from Veech’s personal notes, June 21, 1977
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