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2013
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# 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