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2013
Impact Factor

Alessandro Fortunati

Bristol BS8 1TW, United Kingdom
School of Mathematics, University of Bristol

Publications:

Fortunati A., Wiggins S.
A Kolmogorov Theorem for Nearly Integrable Poisson Systems with Asymptotically Decaying Time-dependent Perturbation
2015, vol. 20, no. 4, pp.  476-485
Abstract
The aim of this paper is to prove the Kolmogorov theorem of persistence of Diophantine flows for nearly integrable Poisson systems associated to a real analytic Hamiltonian with aperiodic time dependence, provided that the perturbation is asymptotically vanishing. The paper is an extension of an analogous result by the same authors for canonical Hamiltonian systems; the flexibility of the Lie series method developed by A. Giorgilli et al. is profitably used in the present generalization.
Keywords: Poisson systems, Kolmogorov theorem, aperiodic time dependence
Citation: Fortunati A., Wiggins S.,  A Kolmogorov Theorem for Nearly Integrable Poisson Systems with Asymptotically Decaying Time-dependent Perturbation, Regular and Chaotic Dynamics, 2015, vol. 20, no. 4, pp. 476-485
DOI:10.1134/S1560354715040061
Fortunati A., Wiggins S.
Persistence of Diophantine Flows for Quadratic Nearly Integrable Hamiltonians under Slowly Decaying Aperiodic Time Dependence
2014, vol. 19, no. 5, pp.  586-600
Abstract
The aim of this paper is to prove a Kolmogorov type result for a nearly integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists in the possibility to choose an arbitrarily small decaying coefficient consistently with the perturbation size.
The proof, based on the Lie series formalism, is a generalization of a work by A. Giorgilli.
Keywords: Hamiltonian systems, Kolmogorov theorem, aperiodic time dependence
Citation: Fortunati A., Wiggins S.,  Persistence of Diophantine Flows for Quadratic Nearly Integrable Hamiltonians under Slowly Decaying Aperiodic Time Dependence, Regular and Chaotic Dynamics, 2014, vol. 19, no. 5, pp. 586-600
DOI:10.1134/S1560354714050062
Fortunati A., Wiggins S.
Normal Form and Nekhoroshev Stability for Nearly Integrable Hamiltonian Systems with Unconditionally Slow Aperiodic Time Dependence
2014, vol. 19, no. 3, pp.  363-373
Abstract
The aim of this paper is to extend the result of Giorgilli and Zehnder for aperiodic time dependent systems to a case of nearly integrable convex analytic Hamiltonians. The existence of a normal form and then a stability result are shown in the case of a slow aperiodic time dependence that, under some smallness conditions, is independent of the size of the perturbation.
Keywords: Hamiltonian systems, Nekhoroshev theorem, aperiodic time dependence
Citation: Fortunati A., Wiggins S.,  Normal Form and Nekhoroshev Stability for Nearly Integrable Hamiltonian Systems with Unconditionally Slow Aperiodic Time Dependence, Regular and Chaotic Dynamics, 2014, vol. 19, no. 3, pp. 363-373
DOI:10.1134/S1560354714030071

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