Publications/Preprints
Complex Dynamical Systems
- (with Eric Bedford) Dynamics of Rational Surface Automorphisms : Linear Fractional Recurrences, To appear in Journal of Geometric Analysis, preprint
Companion Mathematica notebooks (More will be updated soon.)
1. Invariant cubic
- (with Nina Abarenkova et al.) Degree Complexity of a Family of Birational Maps, To appear in Mathematical Physics, Analysis and Geometry, preprint
- (with Eric Bedford) Degree Growth of Matrix Inversion: Birational Maps of Symmetric, Cyclic Matrices, To appear in Discrete and Contiuous Dynamical Systems Arxiv version
- (with Eric Bedford) Linear Recurrences in the Degree Sequences of Monomial Mappings, To appear in Ergodic Theory and Dynamical Systems , Arxiv version
- (with Eric Bedford) Periodicities in Linear Fractional Recurrences: Degree growth of birational surface maps, Michigan Math. J. 54(3), 647-671 2006 Arxiv version
- (with Eric Bedford) On the Degree Growth of Birational Mappings in Higher Dimension, Journal of Geometric Analysis 14(4), 567-596 2004 Arxiv version
- (with Eric Bedford) The Number of Periodic Orbits of a Rational Difference Equation 2007 Submitted for publication, Arxiv version
- (with Eric Bedford) Continuous Families of Rational Surface Automorphisms with Positive Entropy 2008 preprint, Arxiv version
- (with Eric Bedford) Degree Growth of Linear Fractional Recurrences: Critical Cases, In preparation
Stochastic Analysis and Its Applications
- Moment Generating function of the inverse of integral of geometric Brownian Motion, Proc. Amer. Math. Soc. 132, 2753-2759 2004
- (with Jungmin Choi) The derivatives of Asian call option prices, To appear in Communications in Mathematical Sciences preprint
- (with Victor W. Goodman) Exponential Martingales and Time Integrals of Brownian motion 2006 Submitted for publication preprint
- (with Victor W. Goodman) One-Factor Term Structure Without Forward Rates 2006 Submitted for publication preprint
- Integrals of Exponential Brownian motion and Derivative priding in the log-normal bond model, Doctorate thesis 2003
Lie Algebra
- (with Dong-Uy Shin) The recursive dimension formula for graded Lie algebra and its applications, Communications in algebra, 27(6), 2627-2652 1999
- The recursive dimension formula for graded Lie algebra and its applications, Master's thesis 1997