Multivalued mappings and Filippov's operation
Nonlinear differential algebraic equations.
Normal forms for singularities of one dimensional holomorphic vector fields.
Normal forms of analytic perturbations of quasihomogeneous vector fields: Rigidity, invariant analytic sets and exponentially small approximation
In this article, we study germs of holomorphic vector fields which are “higher order” perturbations of a quasihomogeneous vector field in a neighborhood of the origin of , fixed point of the vector fields. We define a “Diophantine condition” on the quasihomogeneous initial part which ensures that if such a perturbation of is formally conjugate to then it is also holomorphically conjugate to it. We study the normal form problem relatively to . We give a condition on that ensures that there...
Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part
We explore the convergence/divergence of the normal form for a singularity of a vector field on with nilpotent linear part. We show that a Gevrey- vector field with a nilpotent linear part can be reduced to a normal form of Gevrey- type with the use of a Gevrey- transformation. We also give a proof of the existence of an optimal order to stop the normal form procedure. If one stops the normal form procedure at this order, the remainder becomes exponentially small.
Normalization of Poincaré singularities via variation of constants.
We present a geometric proof of the Poincaré-Dulac Normalization Theorem for analytic vector fields with singularities of Poincaré type. Our approach allows us to relate the size of the convergence domain of the linearizing transformation to the geometry of the complex foliation associated to the vector field.
Note on canonical forms for functional-differential equations.
Note on Kummer's transformation
On a canonical two-dimensional space of continuous functions
On a certain result of J. D. Keckic.
On a certain transformation of the solution set of two linear second order differential equations
On a codimension 3 bifurcation of plane vector fields with symmetry
On a distribution of zeros of solutions of a fourth-order iterated linear differential equation
On a reduction of nonlinear ordinary differential equations at an irregular type singularity
On a structure of the intersection of the set of dispersions of two second-order linear differential equations
On a transformation of solutions of the differential equation with a complex coefficient of a real variable
On algebraic properties of dispersions of the 3rd and 4th kind of the differential equation
On an application of the generalized Floquet theory to the transformation of the equation into its associated equation
On certain properties of linear iterative equations
An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained,...
On computer-aided solving differential equations and stability study of markets.