2,595 research outputs found
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 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
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
of a nilpotent operator field over a manifold of dimension 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 provides us with a sufficient condition for the integrability of the
eigen-distributions of an operator field over an -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
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