This monograph presents a systematic analysis of the singularities in the transition processes for dynamical systems. We study general dynamical systems, with dependence on a parameter, and construct relaxation times that depend on three variables: Initial conditions, parameters
of the system,
and accuracy
of the relaxation.
We study the singularities of relaxation times as functions of
under fixed
,
and then classify the
bifurcations (explosions) of limit sets.
We study the relationship between singularities of relaxation
times and bifurcations of limit sets. An analogue of the
Smale order for general dynamical systems under perturbations is
constructed. It is shown that the perturbations simplify the
situation: the interrelations between the singularities of
relaxation times and other peculiarities of dynamics for general
dynamical system under small perturbations are the same as for the
Morse-Smale systems.
