Persistence of Invariant Tori in Integrable Hamiltonian Systems Under Almost Periodic Perturbations
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Nonlinear Science"
DOI: 10.1007/s00332-018-9467-9
Abstract: In this paper, we are concerned with the existence of invariant tori in nearly integrable Hamiltonian systems $$\begin{aligned} H=h(y)+f(x,y,t), \end{aligned}$$H=h(y)+f(x,y,t),where $$y\in D\subseteq \mathbb {R}^n$$y∈D⊆Rn with D being an open bounded domain, $$x\in \mathbb {T}^n$$x∈Tn, f(x, y, t)… read more here.
Keywords: persistence invariant; almost periodic; mathbb; hamiltonian systems ... See more keywords
Parabolic invariant tori in quasi-periodically forced skew-product maps
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DOI: 10.1016/j.jde.2020.12.032
Abstract: Abstract We consider the existence of parabolic invariant tori for a class of quasi-periodically forced analytic skew-product maps φ : R n × T d → R n × T d : φ ( z… read more here.
Keywords: invariant tori; order; parabolic invariant; order average ... See more keywords
Invariant tori in dissipative hyperchaos.
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DOI: 10.1063/5.0119642
Abstract: One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional unstable fixed points and… read more here.
Keywords: periodic orbits; invariant tori; tori; tori dissipative ... See more keywords
Persistence of lower dimensional invariant tori in a class of reversible systems
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DOI: 10.1080/14689367.2017.1298725
Abstract: ABSTRACT In this paper we prove the persistence of lower dimensional invariant tori for a class of reversible systems without any non-degeneracy condition. In the proof, we use the special nature that the dimension of… read more here.
Keywords: lower dimensional; invariant tori; persistence lower; dimensional invariant ... See more keywords
Nonchaotic laser pulse dissociation through deformed tori.
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DOI: 10.1103/physreve.101.022207
Abstract: We consider the nonlinear classical dynamics of a diatomic molecule under the action of a laser field in the framework of the driven Morse oscillator model. We investigate the influence of the dipole function and… read more here.
Keywords: laser; dissociation; laser pulse; nonchaotic laser ... See more keywords
Families of invariant tori in KAM theory: Interplay of integer characteristics
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DOI: 10.1134/s156035471706003x
Abstract: The purpose of this brief note is twofold. First, we summarize in a very concise form the principal information on Whitney smooth families of quasi-periodic invariant tori in various contexts of KAM theory. Our second… read more here.
Keywords: invariant tori; families invariant; tori kam; theory interplay ... See more keywords
Gevrey-smoothness of lower dimensional hyperbolic invariant tori for nearly integrable symplectic mappings
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-017-1307-1
Abstract: This paper provides a normal form for a class of lower dimensional hyperbolic invariant tori of nearly integrable symplectic mappings with generating functions. We prove the persistence and the Gevrey-smoothness of the invariant tori under… read more here.
Keywords: nearly integrable; dimensional hyperbolic; tori nearly; lower dimensional ... See more keywords