Related papers: The Hamiltonian Normal Form
Universal bi-Hamiltonian hierarchies of group-invariant (multicomponent) soliton equations are derived from non-stretching geometric curve flows $\map(t,x)$ in Riemannian symmetric spaces $M=G/H$, including compact semisimple Lie groups…
We give a constructive proof of the existence of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov's normalization algorithm to the case of planetary systems, for which…
We apply the general normal form theorems in Kolmogorov spaces to three classical cases: deformations of hypersurface singularities, normal forms of vector fields and invariant tori in Hamiltonian systems.
The ``Fundamental Theorem" given by Arnold in [2] asserts the persistence of full dimensional invariant tori for 2-scale Hamiltonian systems. However, persistence in multi-scale systems is much more complicated and difficult. In this paper,…
A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of…
In [3] (Rend. Lincei Mat. Appl. 26 (2015), 1-10; see also arXiv:1503.08145 [math.DS]) the following result has been announced: Theorem. Consider a real-analytic nearly-integrable mechanical system with potential $f$, namely, a Hamiltonian…
In this paper, we introduce the notion of the stability of automorphic forms for the general linear group and relate the stability of automorphic forms to the moduli space of real tori and the Jacobian real locus.
With the modified Riemann-Liouville fractional derivative, a fractional Tu formula is presented to investigate generalized Hamilton structure of fractional soliton equations. The obtained results can be reduced to the classical Hamilton…
Chow, Li and Yi in [2] proved that the majority of the unperturbed tori {\it on sub-manifolds} will persist for standard Hamiltonian systems. Motivated by their work, in this paper, we study the persistence and tangent frequencies…
In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent…
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give…
We show that an analytic invariant torus $\cT_0$ with Diophantine frequency $\o_0$ is never isolated due to the following alternative. If the Birkhoff normal form of the Hamiltonian at $\cT_0$ satisfies a R\"ussmann transversality…
We prove a new invariant torus theorem, for $\alpha$-Gevrey smooth Hamiltonian systems, under an arithmetic assumption which we call the $\alpha$-Bruno-R\"ussmann condition, and which reduces to the classical Bruno-R\"ussmann condition in…
We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative perodic orbits near a relative equilibrium in a Hamiltonian system…
A section of a Hamiltonian system is a hypersurface in the phase space of the system, usually representing a set of one-sided constraints (e.g. a boundary, an obstacle or a set of admissible states). In this paper we give local…
Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie…
In this paper we obtain exact normal forms with functional invariants for local diffeomorphisms, under the action of the symplectomorphism group in the source space. Using these normal forms we obtain exact classification results for the…
Higher order normalizations are performed in the generalized photogravitational restricted three body problem with Poynting-Robertson drag. In this problem we have taken bigger primary as a source of radiation and smaller primary as an…
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…
In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to very general situations including nonholonomic mechanical…