I am interested in dynamical systems theory and ergodic theory of holomorphic maps on complex manifolds or on algebraic varieties. Complex manifolds and algebraic varieties are known to have very beautiful geometric structures. On the other hand, dynamical systems theory and ergodic theory deal with very complicated figures, chaos and fractals, created by iterations of a mapping. The fusion of these two fields enables us to feel the double joy of drawing an extremely complicated figure on a space of extremely simple beauty. As applications of these, I am working on the complex dynamics of nonlinear differenatial equations called Painlevé equations. Painlevé equations are nonlinear analogues of hypergeometric equations which are classically well-known linear equations. Because of their nonlinearity, Painlevé equations exhibit chaotic behaviors which cannot be observed in hypergeometric equations, a feature that interests me very much!
- K. Iwasaki,
Finite branch solutions to Painleve VI around a fixed singular point,
Adv. Math. 217 (2008), no. 5, 1889–1934.
- K. Iwasaki and T. Uehara,
Periodic points for area-preserving birational maps of surfaces,
Math. Z. 266 (2010), no. 2, 289–318.
- K. Iwasaki,
Cubic harmonics and Bernoulli numbers,
J. Combinatorial Theory, Ser. A. 119 (2012), no. 6, 1216–1234.