共查询到20条相似文献,搜索用时 0 毫秒
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Doklady Mathematics - 相似文献
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Christian Bonatti 《Topology》2005,44(3):475-508
The known examples of transitive partially hyperbolic diffeomorphisms on 3-manifolds belong to 3 basic classes: perturbations of skew products over an Anosov map of T2, perturbations of the time one map of a transitive Anosov flow, and certain derived from Anosov diffeomorphisms of the torus T3. In this work we characterize the two first types by a local hypothesis associated to one closed periodic curve. 相似文献
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We give a complete invariant, called global scheme, of topological conjugacy classes of gradient-like diffeomorphisms, on compact 3-manifolds. Conversely, we can realize any abstract global scheme by such a diffeomorphism. 相似文献
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The present paper is the first step in the study of Morse-Smale diffeomorphisms with heteroclinic orbits (i.e.,which are non-gradient-like)on 3-manifolds. We give a complete classification of the simplest of such diffeomorphisms.Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 7, Suzdal Conference-1, 2003.This revised version was published online in April 2005 with a corrected cover date. 相似文献
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In a very general setting, we show that a 3-manifold obtained as the orbit space of the basin of a topological attractor is either S2×S1 or irreducible.We then study in more detail the topology of a class of 3-manifolds which are also orbit spaces and arise as invariants of gradient-like diffeomorphisms (in dimension 3). Up to a finite number of exceptions, which we explicitly describe, all these manifolds are Haken and, by changing the diffeomorphism by a finite power, all the Seifert components of the Jaco-Shalen-Johannson decomposition of these manifolds are made into product circle bundles. 相似文献
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A. Prishlyak 《Journal of Mathematical Sciences》2007,144(5):4492-4499
We construct a topological invariant for the canonical decomposition on prime and round handles associated with a Morse-Smale
flow on a closed 3-manifold. We prove that the flows are topologically equivalent if and only if their invariants coincide.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 185–196, 2005. 相似文献
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In this paper, we obtain the topological classification of gradient-like diffeomorphisms and the conditions of topological conjugacy of Morse-Smale diffeomorphisms with finite sets of heteroclinic trajectories on three-dimensional manifolds.Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 73–80, January, 1996.This research was partially supported by the Russian Foundation for Basic Research under grant No. 93-01-01-407, by the International Science Foundation under grant R99000, and by the Foundation Cultural Initiative. 相似文献
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V. Z. Grines E. Ya. Gurevich V. S. Medvedev 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):59-83
Let M n be a closed orientable manifold of dimension greater than three and G 1(M n ) be the class of orientation-preserving Morse-Smale diffeomorphisms on M n such that the set of unstable separatrices of every f ∈ G 1(M n ) is one-dimensional and does not contain heteroclinic orbits. We show that the Peixoto graph is a complete invariant of topological conjugacy in G 1(M n ). 相似文献
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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
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