Symmetries and Singularity Structures

These lectures deal with background and latest developments in symmetries, singularity structures (Painleve analysis) and their reaction to integrability and chaos in classical and quantum nonlinear dynamical systems. The book should be useful to both newcomers and senior researchers in physics and mathematics working in the field of nonlinear dynamics. Starting from simple Lie symmetries, the role of generalized Lie and Lie-Backlund symmetries and the underlying algebras associated with a wide spectrum of nonlinear systems are studied. Some keywords are: master symmetries, dynamical symmetries, Kac-Moody and Virasoro algebras, quantum groups, integrable quantum spin chains, bi-Hamiltonian structure of integrable systems and singularity structure analysis of Hamiltonian and non-Hamiltonian systems, the connection between symmetry, solutions quantum chaos and random matrix theory, applications of solitons in plasmas, 4HE films, Josephson junctions and in chemical compounds.