Normal forms à la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium

Alessandro  Fortunati; Stephen  Wiggins

doi:10.3934/dcdss.2016044

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2016, Volume 9, Issue 4: 1109-1118. Doi: 10.3934/dcdss.2016044

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Normal forms à la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium

Alessandro Fortunati^1, and
Stephen Wiggins^1,

1.
School of Mathematics, University of Bristol, Bristol BS8 1TW

Received: February 28, 2015

Revised: July 31, 2015

Published: July 2016

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Abstract

The classical theorem of Moser, on the existence of a normal form in the neighbourhood of a hyperbolic equilibrium, is extended to a class of real-analytic Hamiltonians with aperiodically time-dependent perturbations. A stronger result is obtained in the case in which the perturbing function exhibits a time decay.

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Mathematics Subject Classification: Primary: 37J40; Secondary: 70H09.

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References

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