The aim of this paper was to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them we consider ...

Summary. The aim of this paper is to give an axiomatic definition of the topological entropy for continuous interval maps and, in such a way, to shed some more light on the importance of the different properties of the ...

For planar polynomial vector fields of the form (-y+X(x,y))¿¿x+(x+Y(x,y))¿¿y, where X and Y start at least with terms of second order in the variables x and y, we determine necessary and sufficient conditions under which ...

We study the planar central configurations of the 1 +n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2=n=4. Numerically, ...

In Geometriae Dedicata 79 (2000), 101{108, Rudolf Winkel conjectured: For a given algebraic curve f = 0 of degree m > 4 there is in general no polynomial vector ¯eld of degree less than 2m ¡ 1 leaving invariant f = 0 ...

In this paper we study the normal forms of polynomial systems having a set of given generic invariant algebraic curves.

Any singular irreducible cubic curve (or simply, cubic) after an affine transformation can be written as either y2=x3 , or y2=x2(x+1) , or y2=x2(x-1) . We classify the phase portraits of all quadratic polynomial differential ...

We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical problem of Poincaré from dimension ...

In order to investigate polynomial vector ¯elds admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the a±ne plane. In particular, such morphisms may be used to remove ...