Bill Veech's contributions to dynamical systems

DOI10.3934/jmd.2019vzbMath1415.37006OpenAlexW2917413788MaRDI QIDQ2000065

Giovanni Forni, Howard A. Masur, John Smillie

Publication date: 27 June 2019

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jmd.2019v

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) History of dynamical systems and ergodic theory (37-03)

Related Items (1)

Self-similarity and spectral theory: on the spectrum of substitutions

Cites Work

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• Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow
• Lattice point asymptotics and volume growth on Teichmüller space
• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow
• Isolation, equidistribution, and orbit closures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
• Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle
• Counting closed geodesics in moduli space
• Square-tiled cyclic covers
• Exponential mixing for the Teichmüller flow
• Teichmüller curves, triangle groups, and Lyapunov exponents
• A condition for minimal interval exchange maps to be uniquely ergodic
• Ergodicity of billiard flows and quadratic differentials
• The Teichmüller geodesic flow
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture
• Interval exchange transformations and some special flows are not mixing
• Gauss measures for transformations on the space of interval exchange maps
• Interval exchange transformations and measured foliations
• A criterion for a process to be prime
• The billiard in a regular polygon
• A 'minimal', non-uniquely ergodic interval exchange transformation
• Topological transitivity of billiards in polygons
• Non-ergodic interval exchange transformations
• The Furstenberg structure theorem
• A simple map with no prime factors
• Siegel measures
• Moduli spaces of Abelian differentials: the principal boundary, counting problems, and the Siegel-Veech constants
• Billiards on rational-angled triangles
• Affine mappings of translation surfaces: Geometry and arithmetic
• Deviation of ergodic averages for area-preserving flows on surfaces of higher genus
• Most interval exchanges have no roots
• Logarithmic laws and unique ergodicity
• Volumes and Siegel-Veech constants of \({\mathcal{H}}(2G - 2)\) and Hodge integrals
• Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
• Riemann sums and Möbius
• Counting closed geodesics in strata
• Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
• Minimal sets for flows on moduli space
• Infinitely generated Veech groups
• Teichmüller geodesics of infinite complexity.
• Cocycles' stability for partially hyperbolic systems
• Self-joinings for 3-IETs
• Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards
• Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
• On the ergodicity of flat surfaces of finite area
• Free path lengths in quasicrystals
• Zero Lyapunov exponents of the Hodge bundle
• Weak mixing for interval exchange transformations and translation flows
• Asymptotic formulas on flat surfaces
• Invariant distributions for interval exchange transformations
• Échanges d'intervalles et transformations induites
• Reflections on equicontinuity
• Ergodic Actions of the Mapping Class Group
• Dynamics over Teichmüller space
• Simplicial systems for interval exchange maps and measured foliations
• The Metric Theory of Interval Exchange Transformations I. Generic Spectral Properties
• The Metric Theory of Interval Exchange Transformations II. Approximation by Primitive Interval Exchanges
• The Metric Theory of Interval Exchange Transformations III. The Sah-Arnoux-Fathi Invariant
• Boshernitzan's criterion for unique ergodicity of an interval exchange transformation
• Rank two interval exchange transformations
• A Gauss measure on the set of interval exchange transformations
• Topological dynamics
• A Simple Weakly Mixing Transformation with Nonunique Prime Factors
• Deviation for interval exchange transformations
• Planar structures and billiards in rational polygons: the Veech alternative
• Billiards and Teichmüller curves on Hilbert modular surfaces
• Quasimodularity and large genus limits of Siegel-Veech constants
• Periodic points and invariant pseudomeasures for toral endomorphisms
• Veech surfaces and complete periodicity in genus two
• Simple mixing actions with uncountably many prime factors
• Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum ℋ(1,1)
• The Veech Structure Theorem
• Möbius orthogonality for generalized Morse-Kakutani flows
• An extraordinary origami curve
• The cohomological equation for partially hyperbolic diffeomorphisms
• Almost Automorphic Functions on Groups
• APPROXIMATIONS IN ERGODIC THEORY
• The Equicontinuous Structure Relation for Minimal Abelian Transformation Groups
• The Structure of Distal Flows
• Strict Ergodicity in Zero Dimensional Dynamical Systems and the Kronecker-Weyl Theorem Mod 2
• Point-Distal Flows
• Weak mixing directions in non-arithmetic Veech surfaces
• Interval exchange transformations
• Billiards in polygons
• Interval exchange transformations
• On triangular billiards

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