Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfull...Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfully. We pointed out that an explanation of quantum jumps can be found to result from Colombeau solutions of the Schrodinger equation alone without additional postulates.展开更多
The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an appli...The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered.展开更多
<正> This paper introduces a Maslov-type index theory for paths in the symplectic groups, especially for the degenerate paths via rotational perturbation method, therefore gives a full classification of the line...<正> This paper introduces a Maslov-type index theory for paths in the symplectic groups, especially for the degenerate paths via rotational perturbation method, therefore gives a full classification of the linear Hamiltonian systems with continuous, periodic, and symmetric coefficients. Associating this index with each periodic solution, we establish the existence of muhiple periodic solutions of asymptotically linear Hamihonian systems.展开更多
In this paper, we consider the relation of the Morse index of a closedgeodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closedgeodesic c on a Riemannian manifold M with its lin...In this paper, we consider the relation of the Morse index of a closedgeodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closedgeodesic c on a Riemannian manifold M with its linear Poincare map P (a symplectic matrix), weconstruct a symplectic path γ(t) starting from identity I and ending at P, such that the Morseindex of the closed geodesic c equals the Maslov-type index of γ. As an application of this result,we study the parity of the Morse index of any closed geodesic.展开更多
In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian s...In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.展开更多
The authors prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space.Then a direct proof of the iteration formulae for the Masl...The authors prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space.Then a direct proof of the iteration formulae for the Maslov-type indices of symplectic paths is given.展开更多
文摘Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfully. We pointed out that an explanation of quantum jumps can be found to result from Colombeau solutions of the Schrodinger equation alone without additional postulates.
基金Project supported by the National Natural Science Foundation of China (No.10531050) and FANEDD.
文摘The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered.
文摘<正> This paper introduces a Maslov-type index theory for paths in the symplectic groups, especially for the degenerate paths via rotational perturbation method, therefore gives a full classification of the linear Hamiltonian systems with continuous, periodic, and symmetric coefficients. Associating this index with each periodic solution, we establish the existence of muhiple periodic solutions of asymptotically linear Hamihonian systems.
基金Project 10071040 supported by NNSF,200014 supported by Excellent.Ph.D.Funds of ME of ChinaPMC Key Lab.of ME of China
文摘In this paper, we consider the relation of the Morse index of a closedgeodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closedgeodesic c on a Riemannian manifold M with its linear Poincare map P (a symplectic matrix), weconstruct a symplectic path γ(t) starting from identity I and ending at P, such that the Morseindex of the closed geodesic c equals the Maslov-type index of γ. As an application of this result,we study the parity of the Morse index of any closed geodesic.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No.20060390014)
文摘In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.
基金supported by the National Natural Science Foundation of China(Nos.11221091,11471169)the Key Laboratory of Pure Mathematics and Combinatorics,the Ministry of Education of China
文摘The authors prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space.Then a direct proof of the iteration formulae for the Maslov-type indices of symplectic paths is given.
