By Christian Grosche

During this moment variation, a entire evaluate is given for direction integration in - and third-dimensional (homogeneous) areas of continuing and non-constant curvature, together with an enumeration of the entire corresponding coordinate structures which permit separation of variables within the Hamiltonian and within the course vital. The corresponding course quintessential ideas are provided as a tabulation. Proposals bearing on interbasis expansions for spheroidal coordinate platforms also are given. particularly, the circumstances of non-constant curvature Darboux areas are new during this version.

the quantity additionally includes effects at the numerical examine of the houses of numerous integrable billiard structures in compact domain names (i.e. rectangles, parallelepipeds, circles and spheres) in - and three-d flat and hyperbolic areas. particularly, the dialogue of integrable billiards in circles and spheres (flat and hyperbolic area) and in 3 dimensions are new compared to the 1st variation.

moreover, an outline is gifted on a few contemporary achievements within the conception of the Selberg hint formulation on Riemann surfaces, its large generalization, their use in mathematical physics and string conception, and a few additional effects derived from the Selberg (super-) hint formulation.