排序方式: 共有34条查询结果,搜索用时 15 毫秒
1.
Vyacheslav Z. Grines Dmitry S. Malyshev Olga V. Pochinka Svetlana Kh. Zinina 《Regular and Chaotic Dynamics》2016,21(2):189-203
It is well known that the topological classification of structurally stable flows on surfaces as well as the topological classification of some multidimensional gradient-like systems can be reduced to a combinatorial problem of distinguishing graphs up to isomorphism. The isomorphism problem of general graphs obviously can be solved by a standard enumeration algorithm. However, an efficient algorithm (i. e., polynomial in the number of vertices) has not yet been developed for it, and the problem has not been proved to be intractable (i. e., NPcomplete). We give polynomial-time algorithms for recognition of the corresponding graphs for two gradient-like systems. Moreover, we present efficient algorithms for determining the orientability and the genus of the ambient surface. This result, in particular, sheds light on the classification of configurations that arise from simple, point-source potential-field models in efforts to determine the nature of the quiet-Sun magnetic field. 相似文献
2.
V. Z. Grines E. Ya. Gurevich V. S. Medvedev 《Proceedings of the Steklov Institute of Mathematics》2010,270(1):57-79
Let M
n
be a closed orientable manifold of dimension n > 3. We study the class G
1(M
n
) of orientation-preserving Morse-Smale diffeomorphisms of M
n
such that the set of unstable separatrices of any f ∈ G
1(M
n
) is one-dimensional and does not contain heteroclinic intersections. We prove that the Peixoto graph (equipped with an automorphism)
is a complete topological invariant for diffeomorphisms of class G
1(M
n
), and construct a standard representative for any class of topologically conjugate diffeomorphisms. 相似文献
3.
The results obtained in this paper are related to the Palis-Pugh problem on the existence of an arc with finitely or countably many bifurcations which joins two Morse-Smale systems on a closed smooth manifold M n . Newhouse and Peixoto showed that such an arc joining flows exists for any n and, moreover, it is simple. However, there exist isotopic diffeomorphisms which cannot be joined by a simple arc. For n = 1, this is related to the presence of the Poincaré rotation number, and for n = 2, to the possible existence of periodic points of different periods and heteroclinic orbits. In this paper, for the dimension n = 3, a new obstruction to the existence of a simple arc is revealed, which is related to the wild embedding of all separatrices of saddle points. Necessary and sufficient conditions for a Morse-Smale diffeomorphism on the 3-sphere without heteroclinic intersections to be joined by a simple arc with a “source-sink” diffeomorphism are also found. 相似文献
4.
Theoretical and Mathematical Physics - We construct new substantive examples of nonautonomous vector fields on a $$3$$ -dimensional sphere having simple dynamics but nontrivial topology. The... 相似文献
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Vyacheslav Z. Grines Elena Ya. Gurevich Olga V. Pochinka 《Regular and Chaotic Dynamics》2017,22(2):122-135
Separators are fundamental plasma physics objects that play an important role in many astrophysical phenomena. Looking for separators and their number is one of the first steps in studying the topology of the magnetic field in the solar corona. In the language of dynamical systems, separators are noncompact heteroclinic curves. In this paper we give an exact lower estimation of the number of noncompact heteroclinic curves for a 3-diffeomorphism with the so-called “surface dynamics”. Also, we prove that ambient manifolds for such diffeomorphisms are mapping tori. 相似文献
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Vyacheslav Z. Grines Yulia A. Levchenko Vladislav S. Medvedev Olga V. Pochinka 《Regular and Chaotic Dynamics》2014,19(4):506-512
We prove that each structurally stable diffeomorphism f on a closed 3-manifold M 3 with a two-dimensional surface nonwandering set is topologically conjugated to some model dynamically coherent diffeomorphism. 相似文献
10.
We consider the class G 4 of Morse—Smale diffeomorphisms on $ \mathbb{S} $ 3 with nonwandering set consisting of four fixed points (namely, one saddle, two sinks, and one source). According to Pixton, this class contains a diffeomorphism that does not have an energy function, i.e., a Lyapunov function whose set of critical points coincides with the set of periodic points of the diffeomorphism itself. We define a quasi-energy function for any Morse—Smale diffeomorphism as a Lyapunov function with the least number of critical points. Next, we single out the class G 4,1 ? G 4 of diffeomorphisms inducing a special Heegaard splitting of genus 1 of the sphere $ \mathbb{S} $ 3. For each diffeomorphism in G 4,1, we present a quasi-energy function with six critical points. 相似文献