共查询到20条相似文献,搜索用时 0 毫秒
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M. I. Gordin 《Journal of Mathematical Sciences》1997,87(6):4067-4071
The homoclinic group (an invariant with respect to topological conjugacy) for hyperbolic toral automorphisms is determined.
Certain conditions are given for conjugacy of a homeomorphism of a compact space to hyperbolic toral automorphism. Bibliography:
7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 223, 1994, pp. 140–147.
This paper is partially supported by Russian Foundation for Basic Research, grant 94-01-00921.
Translated by V. V. Sadovskaya. 相似文献
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Let G be a group, let M and N be two normal subgroups of G. We denote by Aut N M (G), the set of all automorphisms of G which centralize G/M and N. In this paper we investigate the structure of a group G in which one of the Inn(G) = Aut N M (G), Aut N M (G) ≤ Inn(G) or Inn(G) ≤ Aut N M (G) holds. We also discuss the problem: “what conditions on G is sufficient to ensure that G has a non-inner automorphism which centralizes G/M and N”. 相似文献
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Our aim is to extend existing results about differentiable rigidity of higher rank abelian actions by automorphisms of a torus.
Previous proofs have required an assumption of semisimplicity, that is, that the action is by commuting diagonalizable matrices. Here we introduce a technique that utilizes the unipotent
part of a non-semisimple action, which allows us to discard the semisimplicity assumption. In its place we will make a technical
assumption that the spectrum of the action restricted to leaves of the coarse Lyapunov decomposition is sufficiently narrow. 相似文献
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The points homoclinic to 0 under a hyperbolic toral automorphism form the intersection of the stable and unstable manifolds
of 0. This is a subgroup isomorphic to the fundamental group of the torus. Suppose that two hyperbolic toral automorphisms
commute so that they determine a ℤ2-action, which we assume is irreducible. We show, by an algebraic investigation of their eigenspaces, that they either have
exactly the same homoclinic points or have no homoclinic point in common except 0 itself. We prove the corresponding result
for a compact connected abelian group, and compare the two proofs.
The second author would like to thank the Austrian Academy of Sciences and the Royal Society for partial support while this
work was done. 相似文献
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Simon Waddington 《Monatshefte für Mathematik》1991,112(3):235-248
For a toral automorphism which is ergodic, but not necessarily hyperbolic, we derive asymptotic formulae for the number of closed orbits by analogy with the Prime Number Theorem. A new proof of the uniform distribution of periodic points is also given. 相似文献
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M. I. Gordin 《Journal of Mathematical Sciences》2010,167(4):501-505
For every hyperbolic toral automorphism T, the present author has defined in his previous paper some unbounded T-invariant second-order difference operators related to the so-called homoclinic group of T. These operators were considered in the space L2 with respect to the Haar measure. It is shown in the present paper that such operators give rise to transition semigroups in the space of continuous functions on the torus and generate dynamically invariant Markov processes. This leads almost immediately to a family of invariant measures for the automorphism T.Along with a short discussion, some open questions about properties of these measures are posed. Bibliography: 9 titles. 相似文献
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Brian Marcus 《Monatshefte für Mathematik》1980,89(2):121-129
We prove that the periodic point measures are dense in the space or invariant measures for ergodic toral automorphisms. 相似文献
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A. M. Vershik 《Functional Analysis and Its Applications》1992,26(3):170-173
St.-Petersburg State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 26, No. 3, pp. 22–27, July–September, 1992. 相似文献
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Siddhartha Bhattacharya 《Transactions of the American Mathematical Society》2008,360(12):6319-6329
Let , and let and be two zero-entropy -actions on compact abelian groups by commuting automorphisms. We show that if all lower rank subactions of and have completely positive entropy, then any measurable equivariant map from to is an affine map. In particular, two such actions are measurably conjugate if and only if they are algebraically conjugate.
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We provide a solution to the isomorphism problem for torsion-free relatively hyperbolic groups with abelian parabolics. As
special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished);
and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]). We also give a solution
to the homeomorphism problem for finite volume hyperbolic n-manifolds, for n≥3. In the course of the proof of the main result, we prove that a particular JSJ decomposition of a freely indecomposable
torsion-free relatively hyperbolic group with abelian parabolics is algorithmically constructible. 相似文献
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Local automorphisms 总被引:1,自引:0,他引:1
Randall Crist 《Proceedings of the American Mathematical Society》2000,128(5):1409-1414
We show that any linear map on a finite dimensional CSL algebra which at each point is equal to the value of some automorphism of is either an automorphism or can be factored as an automorphism and the transpose of a self-adjoint summand of . New examples of local mappings are constructed.