Research
My research concerns the dynamics of complex polynomial maps, with particular interest in the combinatorial and geometric structure of the Mandelbrot set and its analytic continuation into Hénon maps. Especially, I am interested in the relationship between geometric structure of the Mandelbrot set and algebraic structure of shift spaces.
Current Projects
Investigating the image of monodromy action in horseshoe locus
The monodromy action of the fundamental group of the horseshoe locus on the shift space is a well-known phenomenon in complex dynamics. In this project, we study the image of this action and its relationship with the geometric structure of the Mandelbrot set.
Generalization of 2-cascade
A 2-cascade is an analogue in symbolic dynamics of period-doubling bifurcations. There are some results on the properties and characterization of 2-cascades in the context of shift spaces. In this project, we aim to generalize the concept of 2-cascade by replacing the base multiplication by 2 with multiplication by an arbitrary integer d ≥ 2. We will investigate the properties of these generalized d-cascades and their implications in symbolic dynamics.
Trajectory designing based on generating partition
In this project, we explore the design of trajectories of given dynamical systems using generating partitions. By leveraging the structure of generating partitions, we aim to develop methods for constructing trajectories with desired properties and behaviors. This research has potential applications in control theory for spacecrafts.
This project is a collaboration with Professor Mai Bando at Kyushu University.
- Research Interests
- Complex dynamics, Hénon maps, monodromy action, symbolic dynamics, subshifts of finite type, sign gyration compatibility condition, 2-cascades, inert automorphisms.
See the Publications&Talks page for a list of my publications and talks.