David Samuel Simmons

Search results

• 2023

  Exact dimensions of the prime continued fraction Cantor set

  Simmons, D. S. & Das, T., 19 May 2023, arXiv.

  Research output: Working paper
• 2022

  Generalised Hausdorff measure of sets of Dirichlet non-improvable matrices in higher dimensions

  Simmons, D. S. & Bakhtawar, A., 9 Jan 2022, arXiv.

  Research output: Working paper › Preprint
• 2020

  Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents

  Simmons, D. S., Chow, S., Ghosh, A., Guan, L. & Marnat, A., 22 Dec 2020, In: Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. 21, Special 2020, p. 643-671 29 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Dynamical Borel-Cantelli lemma for recurrence theory

  Simmons, D. S., Hussain, M., Li, B. & Wang, B., 8 Sept 2020, arXiv.

  Research output: Working paper › Preprint

• Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism

  Simmons, D. S., Das, T., Fishman, L. & Urbański, M., 21 Jul 2020, arXiv.

  Research output: Working paper › Preprint

• Metrical systems of affine forms

  Simmons, D. S., Hussain, M. & Kristensen, S., 2020, In: Journal of Number Theory. 213, p. 67-100

  Research output: Contribution to journal › Article › peer-review

• Schmidt games and Cantor winning sets

  Simmons, D. S., Badziahin, D., Harrap, S. & Nesharim, E., 25 May 2020, arXiv.

  Research output: Working paper › Preprint

• The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers

  Simmons, D. S., Hussain, M. & Bos, P., 27 Oct 2020, arXiv.

  Research output: Working paper › Preprint
• 2019

  Diophantine approximation on curves

  Simmons, D. S., Hussain, M. & Schleischitz, J., 2019, In: ArXiv e-prints.

  Research output: Contribution to journal › Article

• On the dimension spectra of infinite iterated function systems

  Simmons, D. S. & Das, T., 2019, In: ArXiv e-prints.

  Research output: Contribution to journal › Article

• Random walks on homogeneous spaces and Diophantine approximation on fractals

  Simmons, D. S. & Barak, W., 1 May 2019, In: Inventiones Mathematicae. 216, 2, p. 337-394 58 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• The Measure Game

  Simmons, D. S., Crone, L., Fishman, L., Jackson, S. & Schuerger, H., 24 Oct 2019, (Submitted) arXiv.

  Research output: Working paper › Preprint
• 2018

  A Hausdorff measure version of the Jarník-Schmidt theorem in Diophantine approximation

  Simmons, D., May 2018, In: Mathematical Proceedings of the Cambridge Philosophical Society. 164, 3, p. 413-459 47 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Badly approximable vectors and fractals defined by conformal dynamical systems

  Das, T., Fishman, L., Simmons, D. & Urbański, M., 5 Jul 2018, (E-pub ahead of print) In: Mathematical Research Letters.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces

  Fishman, L., Simmons, D. S. & Urbański, M., 11 Jun 2018, In: Memoirs of the American Mathematical Society. 254, 1215, p. 1-150 150 p.

  Research output: Contribution to journal › Article › peer-review

  File

• Diophantine approximation in Kleinian groups: singular, extremal, and bad limit points

  Beresnevich, V., Ghosh, A., Simmons, D. S. & Velani, S., 1 Oct 2018, In: Journal of the London Mathematical Society. 98, 2, p. 306-328 23 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures

  Das, T., Fishman, L., Simmons, D. S. & Urbański, M., Jul 2018, In: Selecta Mathematica, New Series. 24, 3, p. 2165-2206 42 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces

  Fishman, L., Merrill, K. & Simmons, D. S., Nov 2018, In: Selecta Mathematica, New Series. 24, 5, p. 3875-3888 14 p.

  Research output: Contribution to journal › Article › peer-review

• Intrinsic Diophantine approximation on manifolds: General theory

  Fishman, L., Kleinbock, D., Merrill, K. & Simmons, D., Jan 2018, In: Transactions of the American Mathematical Society. 370, p. 577-599 23 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals

  Fishman, L., Merrill, K. & Simmons, D., 1 Jun 2018, In: ANNALS OF COMBINATORICS. 22, 2, p. 271-293 23 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File
• 2017

  Badly approximable points on self-affine sponges and the lower Assouad dimension

  Simmons, D. S., Das, T., Fishman, L. & Urbański, M., 20 Jun 2017, (E-pub ahead of print) In: Ergodic Theory and Dynamical Systems. 20 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Dimension rigidity in conformal structures

  Das, T., Simmons, D. & Urbański, M., 21 Feb 2017, In: Advances in Mathematics. 308, p. 1127-1186 59 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Rational approximation of affine coordinate subspaces of Euclidean space

  Ramírez, F. A., Simmons, D. S. & Sueess, F., 2017, In: Acta Arithmetica.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result

  Das, T. & Simmons, D., Oct 2017, In: Inventiones Mathematicae. 210, 1, p. 85-134 50 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result

  Simmons, D. S. & Das, T., 25 Mar 2017, (Accepted/In press) 42 p.

  Research output: Working paper › Preprint

  File

• Unconventional height functions in simultaneous Diophantine approximation

  Fishman, L. & Simmons, D., 1 Mar 2017, In: Monatshefte fur Mathematik. 182, 3, p. 577-618 42 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File
• 2016

  A Danzer set for Axis Parallel Boxes

  Simmons, D. & Solomon, Y., 1 Jun 2016, In: Proceedings of the American Mathematical Society. 144, 6, p. 2725-2729 5 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Decaying and non-decaying badly approximable numbers

  Broderick, R., Fishman, L. & Simmons, D., 28 Dec 2016, (E-pub ahead of print) In: Acta Arithmetica. 177, p. 143-152 10 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Geometry and dynamics in Gromov hyperbolic metric spaces: With an emphasis on non-proper settings

  Das, T., Simmons, D. & Urbański, M., 15 Apr 2016, (Accepted/In press) American Mathematical Society. 369 p. (Mathematical Surveys and Monographs)

  Research output: Book/Report › Book

  Open Access

  File

• New examples of complete sets, with connections to a Diophantine theorem of Furstenberg

  Bergelson, V. & Simmons, D., 28 Dec 2016, (E-pub ahead of print) In: Acta Arithmetica. 177, 2, p. 101-131 31 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• On interpreting Patterson -: Sullivan measures of geometrically finite groups as Hausdorff and packing measures

  Simmons, D., 1 Dec 2016, In: Ergodic Theory and Dynamical Systems. 36, 8, p. 2675-2686 12 p.

  Research output: Contribution to journal › Article

  File

• Some manifolds of Khinchin type for convergence

  Simmons, D., 4 Feb 2016, (Submitted).

  Research output: Working paper › Preprint

  File

• The Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game

  Fishman, L., Reams, V. & Simmons, D., 1 Oct 2016, In: Journal of Number Theory. 167, p. 169-179 10 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• The Hausdorff measure version of Gallagher's theorem -- closing the gap and beyond

  Simmons, D. S. & Hussain, M., 1 Dec 2016, (Submitted) 10 p.

  Research output: Working paper › Preprint

  File

• The Hurwitz continued fraction expansion as applied to real numbers

  Simmons, D., 24 Jun 2016, (Accepted/In press) In: L’Enseignement Mathématique. 7 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Tukia's isomorphism theorem in CAT(-1) spaces

  Das, T., Simmons, D. & Urbański, M., 31 Dec 2016, In: Annales academiae scientiarum fennicae series a1-Mathematica. 41, p. 659-680 21 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

• Variations on Dirichlet's theorem

  Fishman, L. & Simmons, D., 1 May 2016, In: Journal of Number Theory. 162, p. 11-22 12 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File
• 2015

  A proof of the matrix version of Baker's conjecture in Diophantine approximation

  Das, T. & Simmons, D., 30 Oct 2015, (Submitted) 9 p.

  Research output: Working paper › Preprint

  File

• Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems

  Das, T., Fishman, L., Simmons, D. & Urbański, M., 23 Aug 2015, (Submitted) 28 p.

  Research output: Working paper › Preprint

  File

• Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces

  Fishman, L., Merrill, K. & Simmons, D., 26 Feb 2015, (Unpublished) 9 p.

  Research output: Working paper › Preprint

  File

• Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind

  Fishman, L., Simmons, D. & Urbański, M., Oct 2015, In: Geometriae Dedicata. 178, 1, p. 95-101 7 p.

  Research output: Contribution to journal › Article › peer-review

  File

• Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions

  Fishman, L., Mance, B., Simmons, D. & Urbanski, M., Oct 2015, In: Bulletin of the Australian Mathematical Society. 92, 2, p. 205-213

  Research output: Contribution to journal › Article › peer-review

  File
• 2014

  Bad(s,t) is hyperplane absolute winning

  Nesharim, E. & Simmons, D. S., 2014, In: Acta Arithmetica. 164, 2, p. 145-152 8 p.

  Research output: Contribution to journal › Article › peer-review

  File

• Determinacy and indeterminacy of games played on complete metric spaces

  Fishman, L., Ly, T. & Simmons, D. S., Oct 2014, In: Bulletin of the Australian Mathematical Society. 90, 2, p. 339-351 13 p.

  Research output: Contribution to journal › Article › peer-review

  File

• Diophantine approximation in Banach spaces

  Fishman, L., Simmons, D. S. & Urbański, M., 2014, In: Journal de Théorie des Nombres de Bordeaux. 26, 2, p. 363-384 22 p.

  Research output: Contribution to journal › Article › peer-review

  File