3 options
Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems / by Heinz Hanβmann.
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2366,2368-2379,2381-2382 2385,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Hanbmann, Heinz, author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 1893.
- Lecture Notes in Mathematics, 0075-8434 ; 1893
- Language:
- English
- Subjects (All):
- Differentiable dynamical systems.
- Differential equations.
- Global analysis (Mathematics).
- Dynamical Systems and Ergodic Theory.
- Ordinary Differential Equations.
- Global Analysis and Analysis on Manifolds.
- Theoretical, Mathematical and Computational Physics.
- Local Subjects:
- Dynamical Systems and Ergodic Theory.
- Ordinary Differential Equations.
- Global Analysis and Analysis on Manifolds.
- Theoretical, Mathematical and Computational Physics.
- Physical Description:
- 1 online resource (XVI, 242 pages 22 illustrations).
- Contained In:
- Springer eBooks
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
- System Details:
- text file PDF
- Summary:
- Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Hence, without the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system. The text moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations have to be replaced by Cantor sets. Planar singularities and their versal unfoldings are an important ingredient that helps to explain the underlying dynamics in a transparent way.
- Contents:
- Bifurcations of Equilibria
- Bifurcations of Periodic Orbits
- Bifurcations of Invariant Tori
- Perturbations of Ramified Torus Bundles
- Planar Singularities
- Stratifications
- Normal Form Theory
- Proof of the Main KAM Theorem
- Proofs of the Necessary Lemmata.
- Other Format:
- Printed edition:
- ISBN:
- 9783540388968
- Access Restriction:
- Restricted for use by site license.
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.