منابع مشابه
Maslov Index for Hamiltonian Systems
The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.
متن کاملThe Maslov index for paths
Maslov’s famous index for a loop of Lagrangian subspaces was interpreted by Arnold [1] as an intersection number with an algebraic variety known as the Maslov cycle. Arnold’s general position arguments apply equally well to the case of a path of Lagrangian subspaces whose endpoints lie in the complement of the Maslov cycle. Our aim in this paper is to define a Maslov index for any path regardle...
متن کاملHamilton-Jacobi Approach for Power-Law Potentials
The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, V (q) = αqn, where α and n are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of α, n and the total energy E. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometri...
متن کاملThe Maslov Index Revisited
Abs t r ac t . Let 7) be a Hermitian symmetric space of tube type, S its Shilov boundary and G the neutral component of the group of bi-holomorphic diffeomorphisms of 7). In the model situation 7) is the Siegel disc, S is the manifold of Lagrangian subspaces and G is the symplectic group. We introduce a notion of transversality for pairs of elements in S, and then study the action of G on the s...
متن کاملComputing the Maslov Index for Large Systems
We address the problem of computing the Maslov index for large linear symplectic systems on the real line. The Maslov index measures the signed intersections (with a given reference plane) of a path of Lagrangian planes. The natural chart parameterization for the Grassmannian of Lagrangian planes is the space of real symmetric matrices. Linear system evolution induces a Riccati evolution in 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: JETP Letters
سال: 2017
ISSN: 0021-3640,1090-6487
DOI: 10.1134/s0021364017010106