caa a22 4500 469034793 CHVBK 20180323132753.0 cr unu---uuuuu 170328e19920801xx s 000 0 eng 10.1007/BF01015553 doi (NATIONALLICENCE)springer-10.1007/BF01015553 Semiclassical maslov asymptotics with complex phases. I. General approach [Elektronische Daten] [V. Belov, S. Dobrokhotov] A method of constructing semiclassical asymptotics with complex phases is presented for multidimensional spectral problems (scalar, vector, and with operator-valued symbol) corresponding to both classically integrable and classically nonintegrable Hamiltonian systems. In the first case, the systems admit families of invariant Lagrangian tori (of complete dimension equal to the dimensionn of the configuration space) whose quantization in accordance with the Bohr—Sommerfeld rule with allowance for the Maslov index gives the semiclassical series in the region of large quantum numbers. In the nonintegrable case, families of Lagrangian tori with complete dimension do not exist. However, in the region of regular (nonchaotic) motion, such systems do have invariant Lagrangian tori of dimensionk<n (incomplete dimension). The construction method associates the families of such tori with spectral series covering the region of "intermediate” quantum numbers. The construction includes, in particular, new quantization conditions of Bohr—Sommerfeld type in which other characteristics of the tori appear instead of the Maslov index. Applications and also generalizations of the theory to Lie groups will be presented in subsequent publications of the series. Plenum Publishing Corporation, 1993 Belov V. aut Dobrokhotov S. aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 92/2(1992-08-01), 843-868 0040-5779 92:2<843 1992 92 11232 https://doi.org/10.1007/BF01015553 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01015553 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Belov V. aut NATIONALLICENCE 700 1- Dobrokhotov S. aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 92/2(1992-08-01), 843-868 0040-5779 92:2<843 1992 92 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer