منابع مشابه
Hörmander-Kashiwara and Maslov indices
Given a finite-dimensional symplectic vector space, we first study the fundamentals group of the space of symplectomorphisms and the space of Lagrangians to construct Maslov indices of loops in these spaces. Then we introduce Hörmander-Kashiwara index of a Lagrangian triple and use it to define Maslov indices counting the number of intersections of two paths of Lagrangians or symplectomorphisms...
متن کاملAnti-symplectic Involution and Maslov Indices
We carry out some first steps in setting up a theory for Lagrangian Floer theory, mimicking Seidel’s construction for Hamiltonian Floer homology [7], for the subgroup HamL(M,ω) of Ham(M,ω) which preserves the Lagrangian L. When the symplectic manifold M has anti-symplectic involution c and L is the fixed Lagrangian submanifold, we consider the subgroup Hamc(M,ω) which commute with c. In the lat...
متن کاملStochastic area distributions: optimal trajectories, Maslov indices and asymptotic results
In this paper we study the semi-classical approximation for the distribution of area associated with (i) planar polymer rings constrained to enclose a fixed algebraic area and (ii) planar rings subject to an external electric field and constrained to enclose a fixed algebraic area. We demonstrate that the results are accurate in the asymptotic regime. Moreover, we also show that in case (i) it ...
متن کاملOn the canonically invariant calculation of Maslov indices
After a short review of various ways to calculate the Maslov index appearing in semiclassical Gutzwiller type trace formulae, we discuss a coordinate-independent and canonically invariant formulation recently proposed by A Sugita (2000, 2001). We give explicit formulae for its ingredients and test them numerically for periodic orbits in several Hamiltonian systems with mixed dynamics. We demons...
متن کاملThe Morse and Maslov indices for matrix Hill’s equations
For Hill’s equations with matrix valued periodic potential, we discuss relations between the Morse index, counting the number of unstable eigenvalues, and the Maslov index, counting the number of signed intersections of a path in the space of Lagrangian planes with a fixed plane. We adapt to the one dimensional periodic setting the strategy of a recent paper by J. Deng and C. Jones relating the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2017
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2016.03.021