Christophe Golé Associate Professor Ph.D., Boston University cgole@smith.edu Burton 316 (413) 585 3875

Recent Courses

MTH204, Numerical Methods and Differential Equations
MTH211, Linear Algebra
MTH 224, Topics in Geometry
MTH 243, Introduction to Analysis
MTH 343, Topics in Analysis

Academic Interests

My research interests are in the theory of dynamical systems as it applies to Hamiltonian systems and Mathematical Biology. Dynamical systems is the mathematical theory that studies time evolution of systems. They have been used to model many systems from physics, economics, biology etc. The theory's claim to fame is to be the proper setting to the mathematical notion of chaos.

Hamiltonian systems, is a subfield of dynamical systems that includes Celestial Mechanics and all physical, mechanical systems that conserve energy. A pendulum without friction is a simple example of Hamiltonian system. My research in that field has been centered on finding periodic orbits for these systems. I helped develop variational methods that arise from decomposing the time evolution of the system into finite time steps (leading to symplectic maps). These variational methods have the advantage of being finite dimensional. In this research, I like to use a combination of dynamical systems, linear algebra and algebraic topology, and some ergodic measure theory if I need to. In this context, I came across some strange objects that I baptised ghost tori.

My Mathematical Biology interest is in plant pattern formation (phyllotaxis). One well publicized phenomenon is the very frequent occurrence of Fibonacci numbers of spirals in sunflowers, pine cones and many other plants. My colleagues Pau Atela, Scott Hotton and I have studied different mathematical models where one can prove theorems explaining this phenomenon (as well as others lesser known phenomena). In collaboration with the Smith Botanic Garden, we also created an exhibit "Plant Spiral: Beauty You Can Count On". It is now accessible in virtual form on our Phyllotaxis website, which also contains a variety of informations about phyllotaxis.

Personal Information

I was born in France and raised partly in Northen Africa. I also lived two years in Mexico. Before coming to Smith College, I held positions at U. of Minesota, ETH (Zurich), SUNY Stony Brook and UC Santa Cruz. I directed the Smith Geneva JYA program in 2003-04. You can often see me at the French and Spanish tables (mondays and Wednesdays at Duckett House). I like playing jazz piano and reading. I live in Northampton with my wife Liz and daughter Marguerite.

Representative Publications

Book
Symplectic Twist Maps  (World Scientific, 2001)

Articles
A Dynamical System for Plant Pattern Formation: Rigorous Analysis (with P.Atela and S. Hotton), J. Nonlinear Sci. Vol. 12 , Number 6 (2002)
Lagrangian systems on hyperbolic manifolds (with Boyland, P.)  Ergodic Theory & Dynamical Systems , 19, (1999)
A Note on Carnot Geodesics in Nilpotent  Lie Groups (with R.  Karidi)   J. of Dyn. &  Control Sys. (1995)
Periodic orbits for Hamiltonian systems in cotangent bundles, Trans. AMS.  Vol. 343, number 1, (1994)
More publications

Spiral patterns in a daisy. There are 21 spirals winding in one direction, 34 in the other. Find more about this in the Phyllotaxis website.