Fungsional linier dan ruang dual

Bentuk khusus dari fungsi linier adalah fungsional-linier , yaitu fungsi linier dari su¬atu ruang vektor ke skalar suatu field Himpunan dari fungsionrl-linier akan, membentuk suatu ruang yang disiput Ruang Dual Dan basis-basis dart ruang dual tersebut dina makan Basis Dual ight owner(s) agree that UNDIP-IR: may, withopt rpose of preservation. The author(s) or

Separation of variables in multi-Hamiltonian systems: an application to the Lagrange top

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the reduction of the vector field and of the Poisson tensors. We show explicitly that, after the reduction on each one of the symplectic leaves, the vector field of the Lagrange top is separable in the sense of Hamilton-Jacobi.Comment: report to XVI NEEDS (Cadiz 2002): 15 pages, no figures, LaTeX. To appear in Theor. Math. Phy

Haantjes Algebras of Classical Integrable Systems

A tensorial approach to the theory of classical Hamiltonian integrable systems is proposed, based on the geometry of Haantjes tensors. We introduce the class of symplectic-Haantjes manifolds (or $\omega \mathscr{H}$ manifolds), as the natural setting where the notion of integrability can be formulated. We prove that the existence of suitable Haantjes algebras of (1,1) tensor fields with vanishing Haantjes torsion is a necessary and sufficient condition for a Hamiltonian system to be integrable in the Liouville-Arnold sense. We also show that new integrable models arise from the Haantjes geometry. Finally, we present an application of our approach to the study of the Post-Winternitz system and of a stationary flow of the KdV hierarchy.Comment: 31 page

A New family of higher-order Generalized Haantjes Tensors, Nilpotency and Integrability

We propose a new infinite class of generalized binary tensor fields, whose first representative of is the known Fr\"olicher--Nijenhuis bracket. This new family of tensors reduces to the generalized Nijenhuis torsions of level $m$ recently introduced independently in \cite{KS2017} and \cite{TT2017} and possesses many interesting algebro-geometric properties. We prove that the vanishing of the generalized Nijenhuis torsion of level $(n-1)$ of a nilpotent operator field $A$ over a manifold of dimension $n$ is necessary for the existence of a local chart where the operator field takes a an upper triangular form. Besides, the vanishing of a generalized torsion of level $m$ provides us with a sufficient condition for the integrability of the eigen-distributions of an operator field over an $n$-dimensional manifold. This condition does not require the knowledge of the spectrum and of the eigen-distributions of the operator field. The latter result generalizes the celebrated Haantjes theorem.Comment: 25 page

Quasi-BiHamiltonian Systems and Separability

Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis coordinates) and its separability is proved.Comment: 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May 1997