Global Kolmogorov tori in the planetary N-body problem. Announcement of result [PDF]
, 2014 We improve a result in [L. Chierchia and G. Pinzari, Invent. Math. 2011] by proving the existence of a positive measure set of $(3n-2)$--dimensional quasi--periodic motions in the spacial, planetary $(1+n)$--body problem away from co--planar, circular ...
Pinzari, Gabriella
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Normal Form and Nekhoroshev stability for nearly-integrable Hamiltonian systems with unconditionally slow aperiodic time dependence [PDF]
Regul. Chaotic Dyn., 19(3):363-373, 2014, 2013 The aim of this paper is to extend the results of Giorgilli and Zehnder for aperiodic time dependent systems to a case of general nearly-integrable convex analytic Hamiltonians.
A Bounemoura +21 more
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Stability of relative equilibria with singular momentum values in simple mechanical systems [PDF]
Nonlinearity 19 (2006) 853-877, 2005 A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al.
Arnold V I +14 more
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Weak instability of Hamiltonian equilibria [PDF]
arXiv, 2012 This is an expository paper on Lyapunov stability of equilibria of autonomous Hamiltonian systems. Our aim is to clarify the concept of weak instability, namely instability without non-constant motions which have the equilibrium as limit point as time ...
Zampieri, Gaetano
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On the optimal effective stability bounds for quasi-periodic tori of finitely differentiable and Gevrey Hamiltonians [PDF]
, 2023 The author is grateful to H. Eliasson, T. Seara, and F. Trujillo for valuable discussions and to the referee for useful comments. This work has been supported by the Juan de la Cierva-Formación Program (FJC2021-044720-I) and the Severo Ochoa and María de
Farré Puiggalí, Gerard
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On the dynamics of coupled oscillators and its application to the stability of suspension bridges [PDF]
, 2022 We describe and provide a computer assisted proof of the bifurcation graph for a system of coupled nonlinear oscillator described in a model of a bridge.
Gianni Arioli
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Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium [PDF]
, 2016 The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term.
Alessandro Fortunati +9 more
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Perihelion librations in the secular three--body problem [PDF]
, 2020 A normal form theory for non--quasi--periodic systems is combined with the special properties of the partially averaged Newtonian potential pointed out in [15] to prove, in the averaged, planar three--body problem, the existence of a plenty of motions ...
Pinzari, Gabriella
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Mini-Workshop: Mathematics of Dissipation – Dynamics, Data and Control (hybrid meeting) [PDF]
, 2021 Dissipation of energy --- as well as its sibling the increase of entropy --- are fundamental facts inherent to any physical system. The concept of dissipativity has been extended to a more general system theoretic setting via port-Hamiltonian systems ...
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Stability and Analytic Solutions of an Optimal Control Problem on the Schrödinger Lie Group
Open Physics, 2016 The nonlinear stability and the existence of the periodic solutions for an optimal control problem on the Schrödinger Lie group are discussed. The analytic solutions via optimal homotopy asymptotic method of the dynamics and numerical simulations are ...
Ene Remus-Daniel +2 more
doaj +1 more source