Perturbation theory (dynamical systems)

By Henk W. Broer, H. Hanßmann. 2008

17 citations recorded by the source corpus.

The principle of perturbation theory is to study dynamical systems that are small perturbations of `simple' systems. Here simple may refer to `linear' or `integrable' or `normal form truncation', etc. In many cases general `dissipative' systems can be viewed as small perturbations of Hamiltonian systems. Focussing on Parametrized KAM Theory, persistent occurrence of quasi-periodic tori is established, both inside and outside the class of Hamiltonian systems. Typically perturbation theory explains only part of the dynamics, and in the resulting `gaps' the orderly unperturbed motion is replaced by random or chaotic motion.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics, Optimization & Training

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Simon Lacoste-Julien
2. Francis R. Bach
3. Gauthier Gidel
4. Qiang Yang
5. Yu Zhang
6. Yu Zhang

In Statistical and Nonlinear Physics

1. Simon Lacoste-Julien
2. Gauthier Gidel
3. Francis R. Bach
4. Ioannis Mitliagkas
5. Elad Hazan
6. Waïss Azizian

In Optimization & Training

1. Simon Lacoste-Julien
2. Gauthier Gidel
3. Peter Richtárik
4. Francis R. Bach
5. Nicolas Loizou
6. Sebastian U. Stich
7. Zeyuan Allen-Zhu
8. Martin Jaggi

Citations in the corpus

• Implicit Regularization of Discrete Gradient Dynamics in Deep Linear Neural Networks (2019, background): “The proof can be found for instance in [Berglund, 2001, Lemma 3.1.6] Thus, let us consider W̄1(t) and W̄2(t) the solutions of (58) as well as W̄ 01 (t) and W̄ 0 2 (t) the solutions of the very same differential equation but withB = 0.”