Lior Fishman | Department of Mathematics

Lior Fishman

Research

Published and accepted:

  1. Badly approximable points on self-affine sponges and the lower Assouad dimension
    With: T. Das, D. Simmons and M. Urbanski
    To be published in Ergodic Theory Dynam. Systems

  2. A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation
    With: T. Das, D. Simmons and M. Urbanski
    To be published in C. R. Math. Acad. Sci. Paris

  3. Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures
    With: T. Das, D. Simmons and M. Urbanski
    To be published in Sel. Math. New Ser.

  4. Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces
    With: D. Simmons and M. Urbanski
    To be published in Mem. Amer. Math. Soc.

  5. Badly approximable vectors and fractals defined by conformal dynamical systems
    With: T. Das, D. Simmons and M. Urbanski
    To be published in Math. Res. Lett.

  6. Intrinsic Diophantine approximation on manifolds: general theory
    With: D. Kleinbock, K. Merrill and D. Simmons
    To be published in Trans. Amer. Math. Soc.

  7. Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
    With: K. Merrill and D. Simmons
    ​To be published in Ann. Comb.

  8. Decaying and non-decaying badly approximable numbers
    With: R. Broderick and D. Simmons
    Acta. Arith., 3513 (2017), 143-152

  9. Unconventional height functions in simultaneous Diophantine approximation
    With: D. Simmons
    Monatsh. Math., 182 (2017), no. 3, 587-618

  10. The Banach Mazur Schmidt game and the Banach Mazur McMullen game
    With: V. Reams and D. Simmons
    J. Number Theory, 167 (2016), 169-179

  11. Variations on Dirichlet's theorem
    With: D. Simmons
    J. Number Theory, 162 (2016), 11-22
  12. Shrinking targets for nonautonomous dynamical systems corresponding to Cantor series expansions
    With: B. Mance, D. Simmons and M. Urbanski
    Bull. Aust. Math. Soc., 92 (2015), no. 2, 205-213

  13. Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind
    With: D. Simmons and M. Urbanski
    Geom. Dedicata 178, (2015), 95-101
  14. Extrinsic Diophantine approximation on manifolds and fractals
    With: D. Simmons
    J. Math. Pures Appl. (9) 104 (2015), no. 1, 83-101
  15. Determinacy and indeterminacy of games played on complete metric spaces
    With: T. Ly and D. Simmons
    Bull. Aust. Math. Soc. 90 (2014), 339-351
  16. Diophantine approximation in Banach spaces
    With: D. Simmons and M. Urbanski
    J. Theor. Nombres Bordeaux 26 (2014), no. 2, 363-384
  17. Intrinsic approximation for fractals defined by rational iterated function systems - Mahler's research suggestion
    With: D. Simmons
    Proc. Lond. Math. Soc. (3) 109 (2014), no. 1, 189-212
  18. Diophantine properties of measures invariant with respect to the Gauss map
    With: D. Simmons and M. Urbanski
    J. Anal. Math. 122 (2014), 289-315
  19. Badly Approximable Systems of Affine Forms and Incompressibility on Fractals
    With: R. Broderick and D. Simmons
    J. Number Theory 133 (2013), no. 7, 2186-2205
  20. The set of badly approximable vectors is strongly C^1 incompressible
    With: R. Broderick, D. Kleinbock, A. Reich and B. Weiss
    Math. Proc. Cambridge Philos. Soc., 153 (2012), no 2, 319-339
  21. Intrinsic Approximation on Cantor-like Sets, a Problem of Mahler
    With: R. Broderick and A. Reich
    Mosc. J. Comb. Number Theory, 1 (2011) no.4, 3-12
  22. Schmidt's game, fractals, and orbits of toral endomorphisms
    With: R. Broderick and D. Kleinbock
    Ergodic Theory Dynam. Systems, 31 (2011), no 4, 1095-1107
  23. Schmidt's game, fractals, and numbers normal to no base
    With: R. Broderick, Y. Bugeaud, D. Kleinbock and B. Weiss
    Math. Res. Lett., 17 (2010), no. 2, 307-321
  24. Diophantine approximations on fractals
    With: M. Einsiedler and U. Shapira
    Geom. Funct. Anal., 21 (2011), no. 1,14-35
  25. Schmidt's game, Badly Approximable Matrices and Fractals
    J. Number Theory, 129 (2009), no. 9, 2133-2153
  26. Schmidt's Game on Fractals
    Israel J. Math., 171 (2009), 77-92
  27. Very Small Sets
    With: H. Judah and I. Reclaw
    Colloq. Math., 72 (1998), no. 2, 207-213

Submitted:

  1. Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems
    With: T. Das, D. Simmons and M. Urbanski
  2. Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces
    With: K. Merrill and D. Simmons
  3. Intrinsic Diophantine approximation on quadric hypersurfaces
    With: D. Kleinbock, K. Merrill and D. Simmons
  4. Quantative results using variants of Schmidt's game: dimension bounds, arithmetic progressions and more
    With: R. Broderick and D. Simmons

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