  Nowadays the Lyapunov exponents and Lyapunov dimension have become so
widespread and common that they are often used without references to the
rigorous definitions or pioneering works. It may lead to a confusion since
there are at least two well-known definitions, which are used in computations:
the upper bounds of the exponential growth rate of the norms of linearized
system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds
of the exponential growth rate of the singular values of the fundamental matrix
of linearized system (Lyapunov exponents, LEs). In this work the relation
between Lyapunov exponents and Lyapunov characteristic exponents is discussed.
The invariance of Lyapunov exponents for regular and irregular linearizations
under the change of coordinates is demonstrated.
