Displaying similar documents to “Psi-series of quadratic vector fields on the plane.”

Inverse problems in the theory of analytic planar vector fields.

Natalia Sadovskaia, Rafael O. Ramírez (1998)

Revista Matemática Iberoamericana

Similarity:

In this communication we state and analyze the new inverse problems in the theory of differential equations related to the construction of an analytic planar verctor field from a given, finite number of solutions, trajectories or partial integrals. Likewise, we study the problem of determining a stationary complex analytic vector field Γ from a given, finite subset of terms in the formal power series (...).

Codimension 4 singularities on reflectionally symmetryc planar vector fields.

Freddy Dumortier, Santiago Ibáñez (1999)

Publicacions Matemàtiques

Similarity:

The paper deals with the topological classification of singularities of vector fields on the plane which are invariant under reflection with respect to a line. As it has been proved in previous papers, such a classification is necessary to determine the different topological types of singularities of vector fiels on R whose linear part is invariant under rotations. To get the classification we use normal form theory and the the blowing-up method.

On the analytic non-integrability of the Rattleback problem

H. R. Dullin, A.V. Tsygvintsev (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We establish the analytic non-integrability of the nonholonomic ellipsoidal rattleback model for a large class of parameter values. Our approach is based on the study of the monodromy group of the normal variational equations around a particular orbit. The imbedding of the equations of the heavy rigid body into the rattleback model is discussed.