Dynamical Systems : Limits and Recurrence
DSLR is a reading seminar on dynamical systems.
Its purpose is to approach Hamiltonian dynamics, as studied in symplectic geometry,
from a more dynamical perspective, with a particular focus on understanding the
bifurcation behavior of Hamiltonian orbits.
If you want to join, feel free to contact
tangled@snu.ac.kr.
Participants
- Dongho Lee (SNU, QSMS)
- Wonjun Lee (SNU)
- Chankyu Joung (SNU, BK21)
- Hoon Namgung (Yonsei University)
Textbooks and Papers
-
S. Smale - Differentiable dynamical systems (1967)
A classical paper introducing fundamental concepts of dynamical systems.
-
R. Abraham, J. Marsden - Foundations of Mechanics (1978)
A foundational textbook that develops mechanics in the language of symplectic
geometry, widely used in both mathematics and physics.
-
K. Meyer, G. Hall, D. Offin - Intoduction to Hamiltonian Dynamical Systems and the N-body Problem (1992)
More N-body problems.
-
A. Celletti - Stability and Chaos in Celestial Mechanics (2010)
More celestial mechanics, including KAM theory.
Schedules
Invariant sets and stability
📅 2025-09-09
👤 Dongho Lee (SNU, QSMS)
📍 SNU, 129-104, 17:00 ~ 18:00
In this talk, I will introduce the main topics and basic notions of dynamics.
The notion of limit sets, minimal sets, non-wandering points and recurrent points will be covered.
Also, I will introduce the notion of stable and unstable manifolds of the fixed points.
📑 Note
Return Map and stability of Hamiltonian orbits
📅 2025-09-19
👤 Chankyu Joung (SNU, BK21)
📍 SNU, 129-104, 15:00 ~ 17:00
📑 Note
TBA
📅 2025-11-12
👤 Wonjun Lee (SNU)
📍 SNU, 129-309, 15:00 ~ 17:00
📑 Note
Bifurcation of Hamiltonian Orbits
📅 2025-12-02
👤 Dongho Lee (QSMS, SNU)
📍 SNU, 129-310, 13:00 ~ 15:00
In the 1970s, Meyer and many other mathematicians studied the bifurcation of Hamiltonian orbits, obtaining a number of fundamental results. One of the most important is that, in the generic case, such bifurcations fall into eight well-known types. This classification includes the familiar Lyapunov, birth–death, and period-doubling bifurcations, among others. In this talk, I will review this classical classification of bifurcations, together with several classical theorems used in their analysis, and illustrate them with a few examples. I will also discuss how these classical results relate to the modern theory of symplectic homology. This talk is based primarily on Meyer’s 1970 paper and the book by Abraham and Marsden.
📑 Note
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