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卷 84, 编号 1 (2020)
- 年: 2020
- 文章: 7
- URL: https://bakhtiniada.ru/1607-0046/issue/view/7542
Articles
Valerii Vasil'evich Kozlov (congratulation)
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2020;84(1):3-4
3-4
Linear forms of a given Diophantine type and lattice exponents
摘要
In this paper we prove an existence theorem concerning linear forms of a given Diophantine type and apply it to study the structure of the spectrum of lattice exponents.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2020;84(1):5-26
5-26
On mixed dynamics of two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles
摘要
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.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2020;84(1):27-59
27-59
Two-step sub-Lorentzian structures and graph surfaces
摘要
We establish an area formula for graph mappings on two-step sub-Lorentzian structures with an arbitrary number of spatial and temporal directions. In a particular case, we consider an alternative approach that requires no additional smoothness of the mapping from which the graph is constructed.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2020;84(1):60-104
60-104
Real Kummer quartics and their Heisenberg invariance
摘要
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.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2020;84(1):105-162
105-162
Rigid divisors on surfaces
摘要
We study effective divisors $D$ on surfaces with $H^0(\mathcal{O}_D)=\Bbbk$and $H^1(\mathcal{O}_D)=H^0(\mathcal{O}_D(D))=0$. We give a numerical criterionfor such divisors, following a general investigation of negativity, rigidity and connectivityproperties. Examples include exceptional loci of rational singularities, and spherelikedivisors.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2020;84(1):163-206
163-206
On a strengthening of certain theorems of Gelfond on the integer-valuedness of analytic functions
摘要
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.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2020;84(1):207-230
207-230