We consider the problem of classifying the orbits within a tower of fibrations with P-fibers that generalize the Monster Tower due to Montgomery and Zhitomirskii. The action on the tower is given by prolongations of diffeomorphism germs of 3-space. As a corollary we give the first steps towards the problem of classifying Goursat 2-flags of small length. In short, we classify the orbits within t...

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems ...

By a multi-pointed category we mean a category C equipped with a so called ideal of null morphisms, i.e. a class N of morphisms satisfying f ∈ N ∨ g ∈ N ⇒ fg ∈ N for any composable pair f, g of morphisms. Such categories are precisely the categories enriched in the category of pairs X = (X,N) where X is a set and N is a subset of X, whereas a pointed category has the same enrichment, but restri...

The question of the continuous dependence of solutions to an optimal control problem on data (the so-called stability analysis of solutions or well-posedness) is very important from the point of view of practical applications of theory. Indeed, if the problem is related to a physical phenomenon, its data can be considered only an arbitrarily close approximation to exact values. Consequently, if...