Perturbations of Systems Describing the Motion of a Particle in Central Fields

The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.

Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.

Limit Behaviour of Dynamic Rule-based Systems

The paper suggests a classification of dynamic rule-based systems. For each class of systems, limit behavior is studied. Systems with stabilizing limit states or stabilizing limit trajectories are identified, and such states and trajectories are found. The structure of the set of limit states and trajectories is investigated.

Evolution of Sets Systems and Homotopy Groups of Spheres

Симеон Т. Стефанов, Велика И. Драгиева - В работата е изследвана еволюцията на системи от множества върху n-мерната евклидова сфера S^n. Установена е връзката на такива системи с хомотопичните групи на сферите. Получени са някои комбинаторни приложения за многостени.

Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.