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Guang
(Dennis) Yang |
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Visiting
Assistant Professor of Mathematics |
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Web Site
N/A
Contact Information
| Office: |
227 Malott Hall |
| Phone: |
(607) 254-5058 |
| Fax: |
(607) 255-7149 |
| Email: |
gy26@cornell.edu |
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Education
Ph.D. (2008) Cornell University
Research Area: Dynamical systems,
celestial mechanics
My research interests include the analysis of dynamical systems arising
from physical problems and the development of analytical and geometric
methods that facilitate such analysis. For the past several years, my
research activities have revolved around the study of dynamics near
resonance. Highlights of the research topics I have worked on are:
- Continuation of invariant manifolds.
I have developed of a new theory that can continue an invariant manifold
and its stable and unstable manifolds (if applicable) under a finite
change in their governing system, whereas the traditional theory only
considers the persistence of invariant manifolds under small
perturbations. When applied to study dynamics near resonance, this
new theory is able to establish the existence of weakly normally hyperbolic
invariant manifolds and the associated stable and unstable manifolds
in
resonant regions.
- Homoclinic/Heteroclinic Orbits in Resonance.
Based on the existence results summarized in the previous topic, I
construct and analyze different types of homoclinic/heteroclinic orbits
which are transversal intersections of stable and unstable manifolds
of
invariant manifolds in resonant regions. It includes the application
of
existing tools, such as the Melnikov method and Exchange Lemma, and
the
development of new asymptotic methods that can generate higher order
approximation of the stable and unstable manifolds under consideration.
- Orbital dynamics in a uniformly rotating gravitational field.
This physical application serves as a test bed and demonstration of
the
mathematical results developed in the first two topics. Specifically,
it
includes the study of the orbital dynamics in resonant regions, where
an
orbiter's Keplerian mean motion and the rotational rate of the
gravitational field are close to a nonzero rational ratio. My goal
is to
identify 3-dimensional periodic trajectories in a coordinate frame
that
co-rotates with the gravitational field and then study the dynamics
near
these periodic trajectories.
Selected Publications
Continuation of invariant manifolds, preprint.
Homoclinic/heteroclinic orbits and chaos in resonance, in progress.
Orbital dynamics in a uniformly rotating second
degree and order gravitational field, in progress.
Last modified: January 16, 2008
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