منابع مشابه
Hamiltonian Systems on Time Scales
Linear and nonlinear Hamiltonian systems are studied on time scales . We unify symplectic flow properties of discrete and continuous Hamiltonian systems. A chain rule which unifies discrete and continuous settings is presented for our so-called alpha derivatives on generalized time scales. This chain rule allows transformation of linear Hamiltonian systems on time scales under simultaneous chan...
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* Correspondence: tangxh@mail. csu.edu.cn School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410083, Hunan, P.R. China Full list of author information is available at the end of the article Abstract In this article, we establish some stability criteria for the polar linear Hamiltonian dynamic system on time scales x (t) = α(t)x(σ (t)) + β(t)y(t), y (t) ...
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A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of δ-pseudo-differential operators, valid on an arbitrary regular time scale, is introduced. The linear Poisson tensors and the related Hamiltonians are derived. The quadratic Poisson tensors is given by the use of the recursion operators of the Lax hier...
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We establish WKB estimates for 2 × 2 linear dynamic systems with a small parameter ε on a time scale unifying continuous and discrete WKB method. We introduce an adiabatic invariant for 2 × 2 dynamic system on a time scale, which is a generalization of adiabatic invariant of Lorentz’s pendulum. As an application we prove that the change of adiabatic invariant is vanishing as ε approaches zero. ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2000
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.6992