Volume 84, Nº 1 (2020)

We consider one-parameter families (general unfoldings) of two-dimensional reversible diffeomorphisms that contain a diffeomorphism with a symmetric non-transversal heteroclinic cycle. We show that in such families there exist Newhouse intervals of parameters such that the values corresponding to the co-existence of infinitely many stable, completely unstable, saddle and symmetric elliptic periodic orbits are generic (that is, they form Baire second-category sets). Also, the closures of the sets of orbits of different types have non-empty intersections.

We consider two classifications of real Kummer quartics. They use the Heisenberg invariance of Kummerquartics. The first divides the whole variety of real Kummer quartics into four classes according tothe Heisenberg-invariance type and then subdivides each class into subclasses to obtain a deformation classification.This subdivision into subclasses is performed by means of the topological classification of the real parts of realKummer quartics. The second classification deals with the set of real Kummer quartics with a fixed Heisenberggroup. Such a set consists of a continuous part and a discrete part. We describe the deformation classes of thecontinuous part and describe its discrete part.

We consider entire functions of finite order (greater than or equal to 1) which take rational integer values atthe points of a rather general discrete set. We show that under certain conditions all such functionscan only be exponential polynomials of a special form.