Persistence of Invariant Tori in Integrable Hamiltonian Systems Under Almost Periodic Perturbations
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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
Stability radii for real linear Hamiltonian systems with perturbed dissipation
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DOI: 10.1007/s10543-017-0654-0
Abstract: We study linear dissipative Hamiltonian (DH) systems with real constant coefficients that arise in energy based modeling of dynamical systems. We analyze when such a system is on the boundary of the region of asymptotic… read more here.
Keywords: linear hamiltonian; radii real; hamiltonian systems; stability radii ... See more keywords
Periodic Solutions of Asymptotically Linear Autonomous Hamiltonian Systems with Resonance
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DOI: 10.1007/s10884-017-9608-0
Abstract: In this paper we define the index at infinity of an asymptotically linear autonomous Hamiltonian system. We use this index to prove the existence and bifurcation from infinity of periodic solutions of the system. We… read more here.
Keywords: periodic solutions; asymptotically linear; linear autonomous; solutions asymptotically ... See more keywords
An Index Theory with Applications to Homoclinic Orbits of Hamiltonian Systems and Dirac Equations
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DOI: 10.1007/s10884-020-09846-3
Abstract: In this paper, we will define the index pair $$(i_A(B),\nu _A(B))$$ ( i A ( B ) , ν A ( B ) ) by the dual variational method, and show the relationship between the… read more here.
Keywords: dirac equations; index; homoclinic orbits; index theory ... See more keywords
Multiple brake orbits of even Hamiltonian systems on torus
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DOI: 10.1007/s11425-018-9456-9
Abstract: In this paper, we establish a relationship between the Morse index at rest points in the saddle point reduction and the brake-orbit-type Maslov index at corresponding brake orbits. As an application, we give a criterion… read more here.
Keywords: even hamiltonian; brake orbits; orbits even; multiple brake ... See more keywords
On the Reducibility of a Class of Nonlinear Periodic Hamiltonian Systems with Degenerate Equilibrium
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DOI: 10.1007/s12346-020-00396-z
Abstract: In this paper, we prove the existence of periodic solutions of a class of Hamiltonian systems with degenerate equilibriums under small nonlinear periodic perturbations. Actually we prove that the periodic Hamiltonian systems with small perturbations… read more here.
Keywords: reducibility class; periodic hamiltonian; systems degenerate; hamiltonian systems ... See more keywords
Infinitely many solutions for a class of fractional Hamiltonian systems with combined nonlinearities
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DOI: 10.1007/s13324-017-0197-1
Abstract: This paper concerns the existence of infinitely many solutions for the following fractional Hamiltonian systems: $$\begin{aligned} \left\{ \begin{array}{lllll} -_{t}D^{\alpha }_{\infty }(_{-\infty }D^{\alpha }_{t}x(t))-L(t).x(t)+\nabla W(t,x(t))=0,\\ x\in H^{\alpha }({\mathbb R}, {\mathbb R}^{N}), \end{array} \right. \end{aligned}$$-tD∞α(-∞Dtαx(t))-L(t).x(t)+∇W(t,x(t))=0,x∈Hα(R,RN),where $$\alpha \in… read more here.
Keywords: alpha; infinitely many; hamiltonian systems; fractional hamiltonian ... See more keywords
Integrable Hamiltonian Systems with a Periodic Orbit or Invariant Torus Unique in the Whole Phase Space
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DOI: 10.1007/s40598-018-0093-2
Abstract: It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian… read more here.
Keywords: periodic orbit; phase space; hamiltonian systems; integrable hamiltonian ... See more keywords
Line integral solution of Hamiltonian systems with holonomic constraints
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DOI: 10.1016/j.apnum.2017.12.014
Abstract: Abstract In this paper, we propose a second order energy-conserving approximation procedure for Hamiltonian systems with holonomic constraints. The derivation of the procedure relies on the use of the so-called line integral framework . We… read more here.
Keywords: line integral; hamiltonian systems; holonomic constraints; systems holonomic ... See more keywords
A dissipation-preserving scheme for damped oscillatory Hamiltonian systems based on splitting
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DOI: 10.1016/j.apnum.2021.08.001
Abstract: Abstract In this paper, a new dissipation-preserving scheme is established for weakly dissipative perturbations of oscillatory Hamiltonian systems. The system exhibits a nonlinear oscillatory structure. The main oscillation is governed by a matrix M and… read more here.
Keywords: preserving scheme; scheme; hamiltonian systems; oscillatory hamiltonian ... See more keywords
A note on some superintegrable Hamiltonian systems
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DOI: 10.1016/j.geomphys.2016.06.005
Abstract: We consider some examples of superintegrable system which were recently isolated through a differential Galois group analysis. The identity of these systems is clarified and the corresponding Poisson algebras derived. read more here.
Keywords: superintegrable hamiltonian; geometry; note superintegrable; hamiltonian systems ... See more keywords