Paper Search Console

Home Search Page About Contact

Journal Title

Title of Journal: Commun Math Phys

Search In Journal Title:

Abbravation: Communications in Mathematical Physics

Search In Journal Abbravation:

Publisher

Springer-Verlag

Search In Publisher:

DOI

10.1016/0040-9383(87)90039-5

Search In DOI:

ISSN

1432-0916

Search In ISSN:
Search In Title Of Papers:

Multidimensional Continued Fractions Dynamical Re

Authors: Kostya Khanin João Lopes Dias Jens Marklof
Publish Date: 2006/10/10
Volume: 270, Issue: 1, Pages: 197-231
PDF Link

Abstract

The disadvantage of ‘traditional’ multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors Following ideas of Dani Lagarias and KleinbockMargulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space SLd mathbbZ backslash SLd mathbbR the space of lattices of covolume one that indeed yields best possible approximations to any irrational vector The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems As an example we explicitly construct a renormalization scheme for the linearization of vector fields on tori of arbitrary dimension

Keywords:

References

.
Search In Abstract Of Papers:
Other Papers In This Journal:
  1. Statistics of Wave Functions for a Point Scatterer on the Torus
  2. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality
  3. Stability and Duality in $${\mathcal{N}\,{=}\,2}$$ Supergravity
  4. Exponential Mixing for the 3 D Stochastic Navier–Stokes Equations
  5. Binding of Polarons and Atoms at Threshold
  6. Probabilistic Weyl Laws for Quantized Tori
  7. On Perturbations of the Schwarzschild Anti-De Sitter Spaces of Positive Mass
  8. Wall-Crossing, Free Fermions and Crystal Melting
  9. Standing Ring Blow up Solutions to the N-Dimensional Quintic Nonlinear Schrödinger Equation
  10. Laminar Boundary Layers in Convective Heat Transport
  11. There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group
  12. Duality of 2D Gravity as a Local Fourier Duality
  13. Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities
  14. Extended Scaling Relations for Planar Lattice Models
  15. Infinite-Dimensional Schur–Weyl Duality and the Coxeter–Laplace Operator
  16. Phase Boundaries in Algebraic Conformal QFT
  17. On the Singularity of the Free Energy at a First Order Phase Transition
  18. Free Analog of Pressure and Its Legendre Transform
  19. Continuity of the Lyapunov Exponents for Quasiperiodic Cocycles
  20. On the Correlation Function of the Characteristic Polynomials of the Hermitian Wigner Ensemble
  21. Stationary Random Metrics on Hierarchical Graphs Via $${(\min,+)}$$-type Recursive Distributional Equations
  22. Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems
  23. Higgs Bundles and ( A , B , A )-Branes
  24. Inviscid Incompressible Limits of the Full Navier-Stokes-Fourier System
  25. Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data
  26. Dispersive Estimates for Schrödinger Operators in Dimension Two
  27. A Monoidal Category for Perturbed Defects in Conformal Field Theory
  28. On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System
  29. Holomorphic Factorization for a Quantum Tetrahedron
  30. High Energy Limits of Laplace-Type and Dirac-Type EigenFunctions and Frame Flows
  31. The Operator Product Expansion for Perturbative Quantum Field Theory in Curved Spacetime
  32. The Szegő Kernel on a Sewn Riemann Surface
  33. Wave Relations
  34. An Application of Mirror Extensions
  35. Diffusion in a Weakly Random Hamiltonian Flow
  36. Spherical T-Duality
  37. A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals
  38. Lax Pair Equations and Connes-Kreimer Renormalization
  39. SNA’s in the Quasi-Periodic Quadratic Family
  40. On the Geometry of Closed G 2 -Structures
  41. Irreducible Characters of General Linear Superalgebra and Super Duality
  42. Connecting Solutions of the Lorentz Force Equation do Exist
  43. Toric G 2 and Spin (7) Holonomy Spaces from Gravitational Instantons and Other Examples
  44. The Smoluchowski-Kramers Limit of Stochastic Differential Equations with Arbitrary State-Dependent Friction
  45. Dirac Reduction for Poisson Vertex Algebras
  46. Dispersive Estimates for Schrödinger Equations with Threshold Resonance and Eigenvalue
  47. Multipermutation Solutions of the Yang–Baxter Equation
  48. The Shape of Expansion Induced by a Line with Fast Diffusion in Fisher-KPP Equations
  49. Quasicrystals and Almost Periodicity
  50. A Lower Bound on Blowup Rates for the 3D Incompressible Euler Equation and a Single Exponential Beale-Kato-Majda Type Estimate
  51. On the Weak Solutions to the Maxwell–Landau–Lifshitz Equations and to the Hall–Magneto–Hydrodynamic Equations
  52. Spin(7)-Instantons, Cayley Submanifolds and Fueter Sections
  53. Equivariant Comparison of Quantum Homogeneous Spaces
  54. Regular Strongly Typical Blocks of $${\mathcal{O}^{\mathfrak {q}}}$$
  55. Exponential Equations Related to the Quantum ‘ ax + b ’ Group
  56. Twisted Logarithmic Modules of Vertex Algebras
  57. Singular Continuous Spectrum for Singular Potentials
  58. How to Remove the Boundary in CFT – An Operator Algebraic Procedure
  59. Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles
  60. Twistor Theory on a Finite Graph
  61. Triangular Invariants, Three-Point Functions and Particle Stability on the de Sitter Universe
  62. On positive functionals on algebras of test functions for quantum fields
  63. Large Deviations for the Yang-Mills Measure on a Compact Surface
  64. Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data
  65. Periodicity and the Determinant Bundle
Search Result: