Henryk Żołądek

Remarks on "The classification of reversible cubic systems with center"

The paper [Topol. Methods Nonlinear Anal. 4 (1994), 79–136] from the title was very long and rather technical. Nevertheless it has drawn attention of some people who have pointed out to the author some mistakes and inaccuracies. Especially, the author thanks A. P. Sadovski for sending him a list of mistakes. Also the author himself found some misprints, mistakes and one incomplete proof. Moreover, some new results about this subject have appeared meantime.

Orbital formal normal forms for general Bogdanov–Takens singularity☆

Abstract We solve completely the problem of classification of germs of complex planar vector fields with nilpotent singularity with respect to formal orbital equivalence.

The topological proof of Abel-Ruffini theorem

We present a proof of the non-solvability in radicals of a general algebraic equation of degree greater than four. This proof relies on the non-solvability of the monodromy group of a general algebraic function.

Periodic Planar Systems without Periodic Solutions

We construct examples of non-autonomous planar systems of the formdz/dt=zn+pn−1(eit)zn−1+…+p0(eit),pj—polynomials, which do not have periodic solutions. For the Riccati systemdz/dt=z2+reit we express the valuesrj of the parameter for which there is no periodic solution by means of zeroes of some Bessel function.

A remark about homogeneous polynomial maps

We consider homogeneous polynomial maps

Classification of diffeomorphisms of

F\colon {\mathbb R}^{n} \rightarrow {\mathbb R}^{n}

\mathbb S^4

of degree

induced by queternionic Riccati equations with periodic coefficients

p

The Pascal Theorem and some its generalizations

. We classify the pairs

First order linear differential equations with involutive delay and hypergeometric functions

(p,n)