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Coincidence Wecken Property for Nilmanifolds
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作者 Daciberg GON?ALVES Peter WONG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第2期239-244,共6页
Let f, g: X → Y be maps from a compact infra-nilmanifold X to a compact nilmanifold Y with dim X ≥ dim Y. In this note, we show that a certain Wecken type property holds, i.e., if the Nielsen number N(f, g) vanishes... Let f, g: X → Y be maps from a compact infra-nilmanifold X to a compact nilmanifold Y with dim X ≥ dim Y. In this note, we show that a certain Wecken type property holds, i.e., if the Nielsen number N(f, g) vanishes then f and g are deformable to be coincidence free. We also show that if X is a connected finite complex X and the Reidemeister coincidence number R(f, g) = ∞ then f ~ f' so that C(f', g) = {x ∈ X | f'(x) = g(x)} is empty. 展开更多
关键词 Nielsen COINCIDENCE THEORY nilmanifolds
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Nielsen type numbers and homotopy minimal periods for maps on the 3-nilmanifolds
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作者 Jong Bum LEE 《Science China Mathematics》 SCIE 2008年第3期351-360,共10页
For all continuous maps on the 3-nilmanifolds, we give explicit formulae for a complete computation of the Nielsen type numbers NP_n(f)and Nφ_n(f). The most general cases were explored by Heath and Keppelmann and the... For all continuous maps on the 3-nilmanifolds, we give explicit formulae for a complete computation of the Nielsen type numbers NP_n(f)and Nφ_n(f). The most general cases were explored by Heath and Keppelmann and the complementary part is studied in this paper. While studying the homotopy minimal periods of all maps on the 3-nilmanifolds, we also give a complete description of the homotopy minimal periods for all maps on the 3-nilmanifolds, including a correction to Jezierski and Marzantowicz’s result. 展开更多
关键词 homotopy minimal period Nielsen number Nielsen type number NILMANIFOLD 55M20 57S30
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Classification of Special Anosov Endomorphisms of Nil-manifolds
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作者 Seyed Mohsen MOOSAVI Khosro TAJBAKHSH 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第12期1871-1890,共20页
In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ→N/Γbe a covering map of a nil-manifold and denote by A:N/Γ→N/Γthe nil-endomorphism which is homotopic to f.If f is a spe... In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ→N/Γbe a covering map of a nil-manifold and denote by A:N/Γ→N/Γthe nil-endomorphism which is homotopic to f.If f is a special TA-map,then A is a hyperbolic nil-endomorphism and f is topologically conjugate to A. 展开更多
关键词 HYPERBOLICITY Anosov ENDOMORPHISMS SPECIAL Anosov ENDOMORPHISMS TA maps nilmanifolds
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On the density of Birkhoff sums for Anosov diffeomorphisms
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作者 Shaobo Gan Yi Shi Mingyang Xia 《Science China Mathematics》 SCIE CSCD 2022年第2期319-330,共12页
Let f : M → M be an Anosov diffeomorphism on a nilmanifold. We consider Birkhoff sums for a Holder continuous observation along periodic orbits. We show that if there are two Birkhoff sums distributed at both sides o... Let f : M → M be an Anosov diffeomorphism on a nilmanifold. We consider Birkhoff sums for a Holder continuous observation along periodic orbits. We show that if there are two Birkhoff sums distributed at both sides of zero, then the set of Birkhoff sums of all the periodic points is dense in R. 展开更多
关键词 Anosov diffeomorphism Birkhoff sum periodic point NILMANIFOLD
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