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A Formal KAM Theorem for Hamiltonian Systems and Its Application to Hyperbolic Lower Dimensional Invariant Tori
In this paper we reformulate a formal KAM theorem for Hamiltonian systems with parameters under Bruno-Rüssmann condition. The proof is based on KAM...
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The KAM theorem on the modulus of continuity about parameters
In this paper, we study the Hamiltonian systems H ( y , x , ξ , ε ) = 〈 ω ( ξ ), y 〉+ εP ( y , x , ξ , ε ), where ω and P are continuous about ξ . We prove that...
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KAM Tori for the System of Coupled Quantum Harmonic Oscillators with Reversible Perturbations
In the present paper, we establish an infinite dimensional Kolmogorov–Arnold–Moser (KAM) theorem for reversible systems with double normal...
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KAM in Generalized Hamiltonian Systems with Multi-Scales
The paper concerns the persistence of invariant tori in nearly integrable generalized Hamiltonian systems with multi-scales in the integrable part,...
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Quantitative kam Theory, with an Application to the Three-Body Problem
Based on quantitative “ kam theory”, we state and prove two theorems about the continuation of maximal and whiskered quasi-periodic motions to...
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Partial Preservation of Frequencies and Floquet Exponents of Invariant Tori in the Reversible KAM Context 2
We consider the persistence of smooth families of invariant tori in the reversible context 2 of KAM theory under various weak nondegeneracy...
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Efficient and Accurate KAM Tori Construction for the Dissipative Spin–Orbit Problem Using a Map Reduction
We consider the dissipative spin–orbit problem in Celestial Mechanics, which describes the rotational motion of a triaxial satellite moving on a...
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Maximal Tori in Infinite-Dimensional Hamiltonian Systems: a Renormalisation Group Approach
We study the existence of infinite-dimensional invariant tori in a mechanical system of infinitely many rotators weakly interacting with each...
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Persistence of Multiscale Degenerate Invariant Tori for Reversible Systems with Multiscale Degenerate Equilibrium Points
In this paper, we focus on the persistence of degenerate lower-dimensional invariant tori with a normal degenerate equilibrium point in reversible...
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Periodic Solutions and KAM Tori for the Spatial Maxwell Restricted \(N+1\)-Body Problem with Manev Potential
We consider the motion of an infinitesimal mass under the Newtonian attraction of N point masses forming a ring plus a central body where a Manev...
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On the Persistence of Lower-Dimensional Tori in Reversible Systems with Hyperbolic-Type Degenerate Equilibrium Point Under Small Perturbations
This paper focuses on the persistence of lower-dimensional tori in reversible systems with hyperbolic-type degenerate equilibrium point under small...
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The Persistence of Degenerate Lower-Dimensional Tori in Reversible Systems with a Degenerate Normal Equilibrium Point
In this paper we consider the persistence of degenerate lower-dimensional tori in reversible systems with a degenerate normal equilibrium point,...
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Il teorema KAM
Nel presente capitolo diamo la dimostrazione – anzi due dimostrazioni, basate su metodi differenti – del teorema KAM (cfr. la fine del §9.2), sulla...
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Quasi-Periodicity at Transition from Spiking to Bursting in the Pernarowski Model of Pancreatic Beta Cells
This paper studies quasi-periodicity phenomena appearing at the transition from spiking to bursting activities in the Pernarowski model of pancreatic...
