Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
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hdl:2117/15064
Tipus de documentReport de recerca
Data publicació2011-07
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Abstract
In this paper we study the splitting of separatrices phenomenon which arises when one considers a
Hamiltonian System of one degree of freedom with a fast periodic or quasiperiodic and meromorphic
in the state variables perturbation. The obtained results are different from the previous ones in
the literature, which mainly assume algebraic or trigonometric polynomial dependence on the state
variables. As a model, we consider the pendulum equation with several meromorphic perturbations
and we show the sensitivity of the size of the splitting on the width of the analyticity strip of the
perturbation with respect to the state variables. We show that the size of the splitting is exponentially
small if the strip of analyticity is wide enough. Furthermore, we see that the splitting grows as the
width of the analyticity strip shrinks, even becoming non-exponentially small for very narrow strips.
Our results prevent from using polynomial truncations of the meromorphic perturbation to compute
the size of the splitting of separatrices.
CitacióGuardia, M.; Martínez-Seara, M. "Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation". 2011.
URL repositori externhttp://www.ma1.upc.edu/recerca/preprints/2011/
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prepr201103seara.pdf | 427,2Kb | Visualitza/Obre |