Abstract
map in a neighbourhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behaviour of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of Hénon type.
| Original language | English |
|---|---|
| Publisher | Namur center for complex systems |
| Number of pages | 30 |
| Volume | 2 |
| Edition | 15 |
| Publication status | Published - 1 Jan 2015 |
Publication series
| Name | naXys Technical Report Series |
|---|---|
| Publisher | University of Namur |
| No. | 15 |
| Volume | 2 |
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Keywords
- dynamical systems
- Normal forms method
- Control of chaos
- Hamiltonian control
- Symplectic maps
Cite this
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High-order control for symplectic maps. / Sansottera, Marco; Giorgilli, Antonio; Carletti, Timoteo.
15 ed. Namur center for complex systems, 2015. 30 p. (naXys Technical Report Series; Vol. 2, No. 15).Research output: Book/Report/Journal › Other report
TY - BOOK
T1 - High-order control for symplectic maps
AU - Sansottera, Marco
AU - Giorgilli, Antonio
AU - Carletti, Timoteo
PY - 2015/1/1
Y1 - 2015/1/1
N2 - We revisit the problem of control for devices that can be modeled via a symplecticmap in a neighbourhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behaviour of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of Hénon type.
AB - We revisit the problem of control for devices that can be modeled via a symplecticmap in a neighbourhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behaviour of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of Hénon type.
KW - dynamical systems
KW - Normal forms method
KW - Control of chaos
KW - Hamiltonian control
KW - Symplectic maps
M3 - Other report
VL - 2
T3 - naXys Technical Report Series
BT - High-order control for symplectic maps
PB - Namur center for complex systems
ER -