Singular Bohr–Sommerfeld rules for 2D integrable systems

Singular Bohr-sommerfeld Rules for 2d Integrable Systems

In this paper, we describe Bohr-Sommerfeld rules for semi-classical completely integrable systems with 2 degrees of freedom with non degenerate singularities (Morse-Bott singularities) under the assumption that the energy level of the first Hamiltonian is non singular. The more singular case of focus-focus singularities is studied in [27] and [26]. The case of 1 degree of freedom has been studi...

Singular Bohr-Sommerfeld Rules For 2D Integrable Systems

Singular Bohr–sommerfeld Rules for 2d Integrable Systems

– This article gives Bohr–Sommerfeld rules for semiclassical completely integrable systems with two degrees of freedom with non-degenerate singularities (Morse–Bott singularities) under the assumption that the energy level of the first Hamiltonian is non-singular. The more singular case of focus– focus singularities was treated in previous works by San Vũ Ngo. c. The case of one degree of freed...

Singular Bohr-Sommerfeld Rules For 2D Integrable Systems

Singular constrained linear systems

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...