Vol 73, No 2 (2018)

We construct a sequence converging to the solution to the Cauchy problem for a singularly perturbed linear homogeneous differential equation of any order. This sequence is asymptotic in the following sense: the distance (with respect to the norm of the space of continuous functions) between its nth element and the solution to the problem is proportional to the (n + 1)th power of the perturbation parameter.

The Liouville foliation of a system describing the motion of a material point on a 2-dimensional ellipsoid in the field of elastic force is considered. The main goal is to find the Fomenko-Zieschang invariants (isoenergetic molecules) of the system. To do that, the algebraic method of M. P. Kharlamov is used.

The paper presents a short proof that pushdown transducers without input generate periodic sequences. We also provide lower and upper bounds for the maximal period of output sequence that can be generated by a pushdown transducer with fixed characteristics.