Some properties of the global behaviour of conservative low-dimensional systems. (English) Zbl 1188.37019
Cucker, Felipe (ed.) et al., Foundations of computational mathematics, Hong Kong, China, 2008. Selected papers based on the presentations at the international conference of the Society for the Foundations of Computational Mathematics (FoCM), June 16–26, 2008. Cambridge: Cambridge University Press (ISBN 978-0-521-73970-2/pbk). London Mathematical Society Lecture Note Series 363, 162-189 (2009).
This is interesting, useful, survey paper, concerning of some aspects of global behaviour of dynamical systems. On several examples the author shows, that a combination of analytic, symbolic and numerical tools, together with qualitative and topological considerations, can give a reasonably good description. The list of mentioned examples in the paper is:
(i) The Restricted Three-Body Problem;
(ii) The Sitnikov Problem;
(iii) Bifurcations:The Hopf-Saddle-Node Conservative Unfolding;
(iv) A Problem in Fluid Dynamics: The Rayleigh-Bénard Model;
(v) A Paradigmatic Example:The Henon Map.
For the entire collection see [Zbl 1170.13001].
(i) The Restricted Three-Body Problem;
(ii) The Sitnikov Problem;
(iii) Bifurcations:The Hopf-Saddle-Node Conservative Unfolding;
(iv) A Problem in Fluid Dynamics: The Rayleigh-Bénard Model;
(v) A Paradigmatic Example:The Henon Map.
For the entire collection see [Zbl 1170.13001].
Reviewer: Alois Klíč (Praha)
MSC:
| 37C10 | Dynamics induced by flows and semiflows |
| 37J05 | Relations of dynamical systems with symplectic geometry and topology (MSC2010) |
| 37G05 | Normal forms for dynamical systems |
| 37C75 | Stability theory for smooth dynamical systems |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 70F07 | Three-body problems |
