Hamiltonian Flows Associated with Discrete Maps
نویسندگان
چکیده
We call this sequence a dynamical system generated by f and denote by qj the value of q0 = q after j times of the map qj = f (q0). We encounter such systems in various occasion in mathematics, physics and in the nature. All of complex dynamical systems are examples in mathematics. Bäcklund transformations which characterize integrable systems, connection formulae of Stokes geometry E-mail: [email protected] The work is supported in part by the Grant-in-Aid for general Scientific Research from the Ministry of Education, Sciences, Sports and Culture, Japan (No 10640278). E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]
منابع مشابه
A discrete time relativistic Toda lattice
Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Int...
متن کاملDilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems
In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...
متن کاملLiouville Operator Approach to Symplecticity-Preserving RG Method
We present a method to construct symplecticity-preserving renormalization group maps by using the Liouville operator, and obtain correctly reduced symplectic maps describing their long-time behavior even when a resonant island chain appears. There has been a long history to study an asymptotic solution of Hamiltonian flows by means of singular perturbation methods such as the averaging method a...
متن کاملHamiltonian Curve Flows in Lie Groups G ⊂ U (n ) and Vector Nls, Mkdv, Sine-gordon Soliton Equations
A bi-Hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non-stretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield...
متن کاملA Newton descent method for the determination of invariant tori
We formulate a fictitious-time flow equation which drives an initial guess torus to a torus invariant under given dynamics, provided such torus exists. The method is general and applies in principle to continuous time flows and discrete time maps in arbitrary dimension, and to both Hamiltonian and dissipative systems.
متن کامل