Papers

Diophantine approximation by rational numbers of certain parity types, preprint. (with Seul Bee Lee and Lingmin Liao)

The Markoff and Lagrange spectra on the Hecke group H4, preprint. (with Deokwon Sim)

On the Vinogradov bound by the Diophantine type, preprint. (with Byungchul Cha)

Intrinsic Diophantine approximation on circles and spheres, Mathematika, 70  (2024), e12228. (with Byungchul Cha)

Intrinsic Diophantine approximation on the unit circle and its Lagrange spectrum, Ann. Inst. Fourier, 73 (2023), 101-161. (with Byungchul Cha)

Odd-odd continued fraction algorithm, Monatsh. Math., 198 (2022), 323-344. (with Seul Bee Lee and Lingmin Liao)

On the multiple recurrence properties for disjoint systems, Israel J. Math., 247 (2022), 405-431. (with Michihiro Hirayama and Younghwan Son)

On the Diophantine nature of the elements of Cantor sets arising in the dynamics of contracted rotations, Ann. Sc. Norm. Super. Pisa Cl. Sci., 22 (2021), 1691-1704. (with Yann Bugeaud, Michel Laurent and Arnaldo Nogueira)

On the Lévy constants of Sturmian continued fractions,  Pacific J. Math., 315 (2021), 1-25. (with Yann Bugeaud and Seul Bee Lee)

Hausdorff dimension in inhomogeneous Diophantine approximation, Int. Math. Res. Not. IMRN, 2021, 2108-2133. (with Yann Bugeaud, Seonhee Lim and Michał Rams)

Quasi-Sturmian colorings on regular trees, Ergodic Theory Dynam. Systems, 40 (2020), 3403-3419. (with Seul Bee Lee, Seonhee Lim and Deokwon Sim)

Generic point equivalence and Pisot numbers, Ergodic Theory Dynam. Systems, 40 (2020), 3169-3180. (with Shigeki Akiyama and Hajime Kaneko)

Number theoretical properties of Romik's dynamical system, Bull. Korean Math. Soc., 57 (2020), 251-274. (with Byungchul Cha)

Dirichlet uniformly well-approximated numbers, Int. Math. Res. Not. IMRN, 2019, 7691-7732. (with Lingmin Liao)

Continued fraction algorithm for Sturmian colorings of trees, Ergodic Theory Dynam. Systems, 39 (2019), 2541-2569. (with Seonhee Lim)

Long Hitting time for translation flows and L-shaped billiards, J. Mod. Dyn., 14 (2019), 291-353. (with Luca Marchese and Stefano Marmi)

A new complexity function, repetitions in Sturmian words, and irrationality exponents of Sturmian numbers, Trans. Amer. Math. Soc., 371 (2019), 3281-3308. (with Yann Bugeaud)

Some constructions for the higher-dimensional three-distance theorem, Acta. Arith., 184 (2018), 385-411. (with Valérie Berthé)

Randomness criterion $\Sigma$ and its applications, Sankhya A, 80 (2018), 356-384. (with Teturo Kamae and Yu-Mei Xue)

Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential, Fractals, 26 (2018), 1850026. (with Lingmin Liao, Michał Rams and Baowei Wang)

Hausdorff dimension of the set approximated by irrational rotations, Mathematika, 64 (2018), 267-283. (with Michał Rams and Baowei Wang)

On the expansion of real numbers in two integer bases, Ann. Inst. Fourier, 67 (2017), 2225-2235. (with Yann Bugeaud)

On the b-ary expansions of log (1 + 1/a) and e, Ann. Sc. Norm. Super. Pisa Cl. Sci., 17 (2017), 931-947. (with Yann Bugeaud)

On the expansion of real numbers in two multiplicatively dependent bases, Bull. Aust. Math. Soc., 95 (2017), 373–383. (with Yann Bugeaud)

On the construction of continued fraction normal series in positive characteristic, Tokyo J. Math., 39 (2017), 679-694. (with Hitoshi Nakada and Rie Natsui)

Zero-one law of Hausdorff dimensions of the recurrent sets, Discrete Contin. Dyn. Syst., 36 (2016), 5477-5492. (with Bing Li)

On Kurzweil's 0-1 law in inhomogeneous Diophantine approximation, Acta Arith., 173 (2016), 41-57. (with Michael Fuchs)

Distribution of the asset price movement and market potential, J. Stat. Mech., (2015), P07001. (with Stefano Marmi)

A characterization of eventual periodicity, Theoret. Comput. Sci., 581 (2015), 1-8. (with Teturo Kamae)

Subword complexity and Sturmian colorings of regular trees, Ergodic Theory Dynam. Systems, 35 (2015), 461-481. (with Seonhee Lim)

Diophantine type of interval exchange maps, Ergodic Theory Dynam. Systems, 34 (2014), 1990-2017.

Refined shrinking target property of rotations, Nonlinearity, 27 (2014), 1985-1997.

Farey map, Diophantine approximation and Bruhat-Tits tree, Finite Fields Appl., 30 (2014), 14-32. (with Seonhee Lim, Hitoshi Nakada and Rie Natsui)

Bounded type interval exchange maps, Nonlinearity, 27 (2014), 637-645. (with Stefano Marmi)

Kurzweil type metrical Diophantine properties in the field of formal Laurent series, J. Math. Anal. Appl., 407 (2013), 250-262. (with Bo Tan, Baowei Wang and Jian Xu)

Hyperbolic tessellation and colorings of trees, Abstr. Appl. Anal., 2013. Art.ID 706496, 6 pp. (with Seonhee Lim)

A refined Kurzweil type theorem in positive characteristic, Finite Fields Appl., 20 (2013), 64–75. (with Hitoshi Nakada and Rie Natsui)

The convergence of recurrence of blocks for mixing processes, Osaka J. Math., 49 (2012), 1-20.

Metric inhomogeneous diophantine approximation on the field of formal Laurent series, Acta Arith., 150 (2011), 129-142. (with Hitoshi Nakada)

Return time complexity of Sturmian sequences, Theoret. Comput. Sci., 412 (2011), 3413-3417.

Quantitative recurrence properties for group actions, Nonlinearity, 22 (2009), 1-9.

The recurrence time for interval exchange maps, Nonlinearity, 21 (2008), 2201-2210. (with Stefano Marmi)

The first return time properties of an irrational rotation, Proc. Amer. Math. Soc., 136 (2008), 3941-3951. (with Kyewon Koh Park)

A note on the return time of Sturmian sequences, Korean J. Math., 16 (2008), 259–265.

A new version of first return time test of pseudorandomness, J. KSIAM, 12 (2008), 109–118.

Tests of randomness by the gambler's ruin algorithm, Appl. Math. Comput., 199 (2008), 195-210. (with Chihurn Kim and Geon Ho Choe)

The dynamical Borel-Cantelli lemma and the waiting time problems, Indag. Math., 18 (2007), 421-434. (with Stefano Galatolo)

The shrinking target property of irrational rotations, Nonlinearity, 20 (2007) 1637-1643.

The dynamical Borel-Cantelli lemma for interval maps, Discrete Contin. Dyn. Syst., 17 (2007), 891-900.

The recurrence time for ergodic systems with infinite invariant measures, Nonlinearity 19 (2006), 2567-2580. (with Stefano Galatolo and Kyewon Koh Park)

The recurrence time for irrational rotations, Osaka J. Math., 43 (2006), 351-364.

On the law of logarithm of the recurrence time, Discrete Contin. Dyn. Syst., 10 (2004), 581-587. (with Chihurn Kim)

The waiting time for irrational rotations, Nonlinearity 16 (2003), 1861-1868. (with Byeong Ki Seo)

The recurrence of blocks for Bernoulli processes, Osaka J. Math., 40 (2003), 171-186.

The first return time test for pseudorandom numbers, J. Comput. Appl. Math., 143 (2002), 263-274. (with Geon Ho Choe)

Average convergence rate of the first return time, Colloq. Math., 84/85 (2000), 159-171. (with Geon Ho Choe)

Entropy and the randomness of digits of pi, Commun. Korean Math. Soc., 15 (2000), 682-689. (with Geon Ho Choe)

Endomorphisms of subshifts, Commun. Korean Math. Soc. 14 (1999), 717-734. (with Geon Ho Choe, Young-One Kim and Jungseob Lee)

Applications of ergodic theory to pesudorandom numbers, Bull. Korean Math. Soc., 35 (1998), 173-187. (with Geon Ho Choe and Chihurn Kim)