Topological classification of branched coverings of the two-dimensional sphere

1990 ◽  
Vol 52 (1) ◽  
pp. 2832-2846 ◽  
Author(s):  
A. N. Protopopov
Keyword(s):  
Topological Classification ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Branched Coverings

Topological classification of defects in two‐dimensional quasicrystals

1991 ◽  
Vol 32 (5) ◽  
pp. 1408-1414 ◽  
Author(s):  
Yihren Wu ◽  
K. Y. Szeto
Keyword(s):  
Topological Classification ◽  
Two Dimensional

scholarly journals On topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers

2014 ◽  
pp. 17-33 ◽  
Author(s):  
V. Z. Grines ◽  
◽  
Y. A. Levchenko ◽  
O. V. Pochinka ◽  
◽  
...  
Keyword(s):  
Topological Classification ◽  
Two Dimensional ◽  
Dimensional Surface

scholarly journals On periodic mapping data of a two-dimensional torus with one saddle orbit

2019 ◽  
Vol 21 (2) ◽  
pp. 164-174
Author(s):  
Anna A. Bosova ◽  
Olga V. Pochinka
Keyword(s):  
Periodic Orbit ◽  
Nodal Point ◽  
Zeta Functions ◽  
Topological Classification ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Periodic Surface ◽  
Periodic Data ◽  
Surface Diffeomorphism

Periodic data of diffeomorphisms with regular dynamics on surfaces were studied using zeta functions in a series of already classical works by such authors as P. Blanchard, J. Franks, S. Narasimhan, S. Batterson and others. The description of periodic data for gradient-like diffeomorphisms of surfaces were given in the work of A. Bezdenezhnykh and V. Grines by means of the classification of periodic surface transformations obtained by J. Nielsen. V. Grines, O. Pochinka, S. Van Strien showed that the topological classification of arbitrary Morse-Smale diffeomorphisms on surfaces is based on the problem of calculating periodic data of diffeomorphisms with a single saddle periodic orbit. Namely, the construction of filtering for Morse-Smale diffeomorphisms makes it possible to reduce the problem of studying periodic surface diffeomorphism data to the problem of calculating periodic diffeomorphism data with a single saddle periodic orbit. T. Medvedev, E. Nozdrinova, O. Pochinka solved this problem in a general formulation, that is, the periods of source orbits are calculated from a known period of the sink and saddle orbits. However, these formulas do not allow to determine the feasibility of the obtained periodic data on the surface of this kind. In an exhaustive way, the realizability problem is solved only on a sphere. In this paper we establish a complete list of periodic data of diffeomorphisms of a two-dimensional torus with one saddle orbit, provided that at least one nodal point of the map is fixed.

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