103,122 research outputs found
PAESAGGIO/PAESAGGI: UNA VALORIZZAZIONE DIFFICILE
No full textPRESENTAZIONE DEL "LABORATORIO PAESISTICO", UN'AREA DEL MEDIO FRIULI STUDIATA SENZA INTERRUZIONI PER OLTRE TRENTA ANNI, PERCIò EMBLEMATICA DELL'EVOLUZIONE DEI PAESAGGI FRIULANI CONTEMPORANEI E SUA LETTURA IN CHIAVE DI MUSEO DEI LUOGH
Nijenhuis -manifolds and Lenard bicomplexes: a new approach to KP systems.
No full textFrom the MR review by A.Sym: "One of the most important ingredients of the modern theory of integrable Hamiltonian systems in (1+1) dimensions is the concept of recursion operators. It is a general belief that this concept cannot be extended to the case of integrable Hamiltonian systems in (1+2) dimensions (such as the KP or Davey-Stewartson equations). The main goal of this paper is to correct this opinion. Indeed, the authors develop a new formal setting which is based on two important notions: (1) The Nijenhuis G-manifold and (2) their Lenard bicomplexes. Roughly speaking, the Nijenhuis G-manifold (G a Lie group) is a pair (M,G) of two Nijenhuis manifolds satisfying the following condition: G acts on M leaving its Nijenhuis structure (torsion-free tensor field of (1,1) type) invariant. This formal framework leads to a unified construction of recursion operators in (1+1) as well as in (1+2) dimensions. Some concrete realizations of this formal scheme (KdV and KP-hierarchies) are also discussed in the paper.
The quasi-bi-Hamiltonian formulation of the Lagrange top.
No full textStarting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We show that the vector field of the Lagrange top possesses, on the reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set of separation variables for the corresponding Hamilton-Jacobi equation
Separation of variables in multi-Hamiltonian systems. Application to the Lagrange top.
No full textThis paper completes the analysis, started in J.Phys.A 35 (2002) 1741-1750, of the Lagrange top (LT) as a quasi-bi-Hamiltonian system. 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
Generalized Lenard chains and multi-separability of the Smorodinsky-Winternitz system.
No full textWe show that the notion of generalized Lenard chains allows to formulate in a natural way the theory of multi-separable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function and by a Nijenhuis tensor defined on a symplectic manifold guarantees the separation of variables. As an application, we construct such a chain for the case I of the classical Smorodinsky-Winternitz model
Generalized Nijenhuis Torsions and Block-Diagonalization of Operator Fields.
No full textThe theory of generalized Nijenhuis torsions, which extends the classical notions due to Nijenhuis and Haantjes, offers new tools for the study of normal forms of operator fields. We prove a general result ensuring that, given a family of commuting operator fields whose generalized Nijenhuis torsion of level m vanishes, there exists a local chart where all operators can be simultaneously block-diagonalized. We also introduce the notion of generalized Haantjes algebra, consisting of operators with a vanishing higher-level torsion, as a new algebraic structure naturally generalizing standard Haantjes algebras
"Referencing Perelle (tondo)"
No full text"Referencing Perelle (tondo)" by G James Brown is an oil painting on canvas, 91.5 x 91 cm. The painting was executed as a response to the etching, "Circular Landscape", by Gabriel Perelle (1603-77) and Adam Perelle (1640-95). The painting addresses the subject, conceptual focus, style and approach shown in this early print from the standpoint of a contemporary North Queensland artist's perception of the tropical landscape and current issues. By design, the painting critiques the conventions of the early print by comparing them in visual terms to the artist's personal art practice
Reduction of bi-Hamiltonian systems and the separation of variables: an example from the Boussinesq hierarchy.
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