Displaying similar documents to “Maslov indices on the metaplectic group M p ( n ) ”

Generalized Conley-Zehnder index

Jean Gutt (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

The Conley-Zehnder index associates an integer to any continuous path of symplectic matrices starting from the identity and ending at a matrix which does not admit 1 as an eigenvalue. Robbin and Salamon define a generalization of the Conley-Zehnder index for any continuous path of symplectic matrices; this generalization is half integer valued. It is based on a Maslov-type index that they define for a continuous path of Lagrangians in a symplectic vector space ( W , Ω ¯ ) , having chosen a given...

Special Lagrangian linear subspaces in product symplectic space

Małgorzata Mikosz (2004)

Banach Center Publications

Similarity:

The notes consist of a study of special Lagrangian linear subspaces. We will give a condition for the graph of a linear symplectomorphism f : ( ℝ 2 n , σ = ∑ i = 1 n d x i ∧ d y i ) → ( ℝ 2 n , σ ) to be a special Lagrangian linear subspace in ( ℝ 2 n × ℝ 2 n , ω = π * ₂ σ - π * ₁ σ ) . This way a special symplectic subset in the symplectic group is introduced. A stratification of special Lagrangian Grassmannian S Λ 2 n ≃ S U ( 2 n ) / S O ( 2 n ) is defined.

Levi's forms of higher codimensional submanifolds

Andrea D'Agnolo, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Let X ≅ C n , let M be a C 2 hypersurface of X , S be a C 2 submanifold of M . Denote by L M the Levi form of M at z 0 ∈ S . In a previous paper [3] two numbers s ± ⁢ S , p , p ∈ T ˙ S * ⁢ X z 0 are defined; for S = M they are the numbers of positive and negative eigenvalues for L M . For S ⊂ M , p ∈ S × M T ˙ * S X ) , we show here that s ± ⁢ S , p are still the numbers of positive and negative eigenvalues for L M when restricted to T z 0 C ⁢ S . Applications to the concentration in degree for microfunctions at the boundary are given.

On the first sign change in Mertens' theorem

Jan Büthe (2015)

Acta Arithmetica

Similarity:

The function ∑ p ≤ x 1 / p - l o g l o g ( x ) - M is known to change sign infinitely often, but so far all calculated values are positive. In this paper we prove that the first sign change occurs well before exp(495.702833165).

On control problems of minimum time for Lagrangian systems similar to a swing. II Application of convexity criteria to certain minimum time problems

Aldo Bressan, Monica Motta (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

This Note is the Part II of a previous Note with the same title. One refers to holonomic systems Σ = A ⁢ ⋃ U with two degrees of freedom, where the part A can schemetize a swing or a pair of skis and U schemetizes whom uses A . The behaviour of U is characterized by a coordinate used as a control. Frictions and air resistance are neglected. One considers on Σ minimum time problems and one is interested in the existence of solutions. To this aim one determines a certain structural condition Γ which...

On some equations over finite fields

Ioulia Baoulina (2005)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In this paper, following L. Carlitz we consider some special equations of n variables over the finite field of q elements. We obtain explicit formulas for the number of solutions of these equations, under a certain restriction on n and q .