Jurgen Moser. Monotone twist mappings and the calculus of variations. Ergodic Theory Dynam. Systems, 6(3):401-413, 1986. Home/Search Document Not in Database Summary Related Articles Check |
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Symplectic Twist Maps Without Conjugate Points - Bialy, MacKay (Correct)
....how to apply this to the so called outer billiard problem (see [16] It would be reasonable to conjecture that the only outer billiard without conjugate points on the ane plane is the elliptic one. In some cases the lack of compactness can be overcome (see [4] 2] 4. It was proved by J Moser [14] for area preserving twist maps that every such map can be seen as the time one map of an optical Hamiltonian function. This result was generalised in [5] to higher dimensions for those twist maps with symmetric matrix 12 S (see [8] for the proof and discussion) It is not clear what can be said ....
Moser, J., Monotone twist mappings and the calculus of variations, Erg. Th. and Dyn. Sys. 6, (1986) 401-413.
Stability of Minimal Periodic Orbits - Dullin, Meiss (1998) (Correct)
....flows for which the action minimizing equilibrium points or the minimizing periodic orbits are not hyperbolic. This is very similar to our results, but we treat the case of maps with a completely different method. Although it is known that symplectic twist maps have a corresponding time one flow [11], this requires one to treat time dependent Lagrangian flows, which was not done in [2] Linear stability of a periodic orbit is determined by its multipliers. Let fx 1 ; x 2 ; x n g be a periodic orbit with period n, and let x i n = x i . The linearization of the map at this orbit gives ....
J. Moser. Monotone twist mappings and the calculus of variations. Ergodic Theory Dynam. Systems, 6:401--413, 1986.
Positive Kolmogorov-Sinai entropy for the Standard map - Knill (1999) (1 citation) (Correct)
....exponent the infimum taken on the discrete set S n Y n ae Y is the same as the infimum taken on X . 2) Hamiltonian flows. Like for a large class of monotone twist maps, any Standard map is the time one map of a Hamiltonian differential equation with time dependent periodic Hamiltonians [106]. This is also true in higher dimensional cases [11, 49] Since by Theorem (1.2) positive Kolmogorov Sinai entropy is stable under perturbations of the map, there are many real analytic, time dependent periodic potentials V for which the time dependent Hamiltonian system x = V (t; x) has ....
J. Moser. Monotone twist mappings and the calculus of variations. Ergod. Th. Dyn. Sys., 6:401--413, 1986.
The Obstruction Criterion For Non Existence - Of Invariant Circles (Correct)
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Jurgen Moser. Monotone twist mappings and the calculus of variations. Ergodic Theory Dynam. Systems, 6(3):401-413, 1986.
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