Dr. Ayreena Bakhtawar

Ayreena's research lies in the intersection of  Diophantine approximation, Fractal geometry and Ergodic theory and dynamical systems. She is particularly interested in exploring the Hausdorff dimension theory of the fractals and the ergodic theory of dynamical systems that comes from various versions of continued fractions. Her research also investigates  the connection between the continued fractions and Diophantine approximation.

Major / recent publications

[1] Ayreena Bakhtawar, Carlo Carminati and Stefano Marmi, Global and local minima of $\alpha$ Brjuno functions, Monatshefte fur Mathematik, 207(2):197-230, (2025)

[2] Ayreena Bakhtawar, Mumtaz Hussain, Dmitry Kleinbock and Bao-Wei Wang. Metrical properties for the weighted products of multiple partial quotients in continued fractions. Houston Journal of Mathematics, 49(1) (2023), pp.159--194. 

[3] Ayreena Bakhtawar and David Simmons. Hausdorff measure of sets of Dirichlet non-improvable matrices in higher dimensions. Research in Number Theory 9 (2023), no.3, Paper No. 54, 18 pp.

[4] Ayreena Bakhtawar. Hausdorff dimension for the set of points connected with the generalized Jarn'ik--Besicovitch set. Journal of the Australian Mathematical Society, 112(1) (2022), 1--29

[5] Ayreena Bakhtawar, Philip Bos and Mumtaz Hussain. Hausdorff dimension of an exceptional set in the theory of continued fractions. Nonlinearity, 33(6) (2020), 2615--2639

[6] Ayreena Bakhtawar, Philip Bos and Mumtaz Hussain. The sets of Dirichlet non-improvable numbers versus well-approximable numbers. Ergodic Theory and Dynamical Systems, 40(12) (2020), 3217--3235

Link to all papers

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