Non-singular Periodic Flows on T3 and Periodic Homeomorphisms of T2
Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 23-28
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A homeomorphism f of a space M is pointwise periodic if for each m ∈ M there exists an integer k such that fk(m) =m, where fk is the kth iterate of f. Montgomery proves [5] that if M is a connected topological manifold, then f is periodic; i.e., there exists an integer n such that fn = id. Noting this, Weaver [7] proves that if M is an orientable 2-manifold of class C 1, U⊆M open and C ⊆ U a compact connected set and if g : U → M of class C 1is such that (i) g(C) = C and (ii) whenever the derivative of g at points x∈C has rank 2 it is orientation preserving, then f = g|c : C → C periodic implies that all but a finite number of points of C have as least period the period of f.
Hartzman, C. S. Non-singular Periodic Flows on T3 and Periodic Homeomorphisms of T2. Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 23-28. doi: 10.4153/CMB-1981-003-0
@article{10_4153_CMB_1981_003_0,
author = {Hartzman, C. S.},
title = {Non-singular {Periodic} {Flows} on {T3} and {Periodic} {Homeomorphisms} of {T2}},
journal = {Canadian mathematical bulletin},
pages = {23--28},
year = {1981},
volume = {24},
number = {1},
doi = {10.4153/CMB-1981-003-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-003-0/}
}
TY - JOUR AU - Hartzman, C. S. TI - Non-singular Periodic Flows on T3 and Periodic Homeomorphisms of T2 JO - Canadian mathematical bulletin PY - 1981 SP - 23 EP - 28 VL - 24 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-003-0/ DO - 10.4153/CMB-1981-003-0 ID - 10_4153_CMB_1981_003_0 ER -
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