Mapping and dynamical systems

This paper reviews various mapping techniques used in dynamical astronomy. It is mostly dealing with symplectic mappings. It is shown that used mappings can be usually interpreted as symplectic integrators. It is not necessary to introduce any delta functions it is just sufficient to split Hamiltonian into integrable parts. Actually it may be shown that exact mapping with delta function in the Hamiltonian may be non-symplectic. The application to the study of asteroid belt is emphasised but the possible use of mapping in planetary evolution studies, cometary and other problems is shortly discussed.