Advances in UAS for functional differential equations.
Affine invariant conditions for the topological distinction of quadratic systems with a critical point of the 4th multiplicity.
The affine invariant partition of the set of quadratic systems with one finite singular point of the 4th multiplicity with respect to different topological classes is accomplished. The conditions corresponding to this partition are semi-algebraic, i.e. they are expressed as equalities or inequalities between polynomials.
Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems
In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.
Affinity integral manifolds for impulsive differential equations.
Affinor structures in the oscillation theory
In this paper we consider the system of Hamiltonian differential equations, which determines small oscillations of a dynamical system with n parameters. We demonstrate that this system determines an affinor structure J on the phase space TRⁿ. If J² = ωI, where ω = ±1,0, the phase space can be considered as the biplanar space of elliptic, hyperbolic or parabolic type. In the Euclidean case (Rⁿ = Eⁿ) we obtain the Hopf bundle and its analogs. The bases of these bundles are, respectively, the projective...
Algebraic curve solution for second-order polynomial autonomous systems.
Algebraic elements in the transformation theory of 2nd order linear oscillatory differential equations
Algebraic integrability for minimum energy curves
This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed.
Algebraic methods for solving boundary value problems.
By means of the reduction of boundary value problems to algebraic ones, conditions for the existence of solutions and explicit expressions of them are obtained. These boundary value problems are related to the second order operator differential equation X(2) + A1X(1) + A0X = 0, and X(1) = A + BX + XC. For the finite-dimensional case, computable expressions of the solutions are given.
Algebraic methods in the theory of global properties of the oscillatory equations
Algebraic properties of phases of the differential equation
Algebraic Solutions of Differential Equations (p-Curvature and the Hodge Filtration).
Algebraic solutions of the Lamé equation
In this paper we give a summary of joint work with Alexa van der Waall concerning Lamé equations having finite monodromy. This research is the subject of van der Waall's Ph. D. thesis [W].
Algebraic structure of space and field.
Algebraic theory of right invertible operators
Algebraical loops and transformation of variables
Algebraická štruktúra množiny hlavných hyperbolických fáz diferenciálnych rovníc v intervale
Algebraische Theorie der Transformation der linearen Differentialgleichungen
Algorithm 87. A procedure realizing a fourth order one-step method for solving a system of ordinary differential equations
Algorithm 89. A procedure realizing a fourth order one-step method for solving a system of ordinary differential equations of the form y''=f(x,y,y')