We consider the following topological spaces: , , , , , et . Set . An map is a continuous self-map of having the branching point fixed. We denote by the set of periods of all periodic points of . The set is the full periodicity kernel of if it satisfies the following two conditions: (1) If is an map and , then . (2) If is a set such that for every map , implies , then . In this paper we compute the full periodicity kernel of and .
@article{AIF_1996__46_1_219_0, author = {Leseduarte, Carme and Llibre, Jaume}, title = {The full periodicity kernel of the trefoil}, journal = {Annales de l'Institut Fourier}, pages = {219--262}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {1}, year = {1996}, doi = {10.5802/aif.1512}, mrnumber = {1385516}, zbl = {0834.54024}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1512/} }
TY - JOUR TI - The full periodicity kernel of the trefoil JO - Annales de l'Institut Fourier PY - 1996 DA - 1996/// SP - 219 EP - 262 VL - 46 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1512/ UR - https://www.ams.org/mathscinet-getitem?mr=1385516 UR - https://zbmath.org/?q=an%3A0834.54024 UR - https://doi.org/10.5802/aif.1512 DO - 10.5802/aif.1512 LA - en ID - AIF_1996__46_1_219_0 ER -
Leseduarte, Carme; Llibre, Jaume. The full periodicity kernel of the trefoil. Annales de l'Institut Fourier, Volume 46 (1996) no. 1, pp. 219-262. doi : 10.5802/aif.1512. https://aif.centre-mersenne.org/articles/10.5802/aif.1512/
[ALM1] Periodic orbits of maps of Y, Trans. Amer. Math. Soc., 313 (1989), 475-538. | MR: 90c:58145 | Zbl: 0803.54032
, and ,[ALM2] Combinatorial dynamics in dimension one, Advanced Series in Nonlinear Dynamics, Vol. 5, World Scientific, 1993. | MR: 95j:58042 | Zbl: 0843.58034
, and ,[ALMT] Periods and entropy for Lorenz-like maps, Ann. Inst. Fourier, 39-4 (1989), 929-952. | Numdam | MR: 91e:58146 | Zbl: 0678.34047
, , and ,[AM] Linear orderings and the full periodicity kernel for the n-star, J. Math. Anal. Appl., 180 (1993), 599-616. | MR: 95e:58141 | Zbl: 0822.58013
and ,[Ba] An extension of Sharkovskii's Theorem to the n-od, Ergod. Th. & Dynam. Sys., 11 (1991), 249-271. | MR: 92h:58159 | Zbl: 0741.58010
,[BL] Periods of maps on trees with all branching points fixed, Ergodic Th. & Dynam. Sys., 15 (1995), 239-246. | MR: 96e:58126 | Zbl: 0831.58020
and ,[Bc1] Periodic orbits of continuous maps of the circle, Trans. Amer. Math. Soc., 260 (1980), 553-562. | MR: 83c:54057 | Zbl: 0497.54040
,[Bc2] Periods of periodic points of maps of the circle which have a fixed point, Proc. Amer. Math. Soc., 82 (1981), 481-486. | MR: 82h:58042 | Zbl: 0464.54046
,[BGMY] Periodic points and topological entropy of one dimensional maps, Lecture Notes in Math., Springer-Verlag, Heidelberg, 819 (1980), 18-34. | MR: 82j:58097 | Zbl: 0447.58028
, , and ,[Bk1] Periods implying almost all periods for tree maps, Nonlinearity, 5 (1992), 1375-1382. | MR: 94f:58103 | Zbl: 0760.54027
,[Bk2] On some properties of graph maps : spectral descomposition, Misiurewicz conjecture and abstract sets of periods, preprint, Max-Plank-Institut für Mathematik, Bonn.
,[LL1] On the set of periods for σ maps, to appear in Trans. Amer. Math. Soc. | MR: 1316856 | Zbl: 0868.54035
and ,[LL2] On the full periodicity kernel for one-dimensional maps, preprint, 1994,. | MR: 1676930 | Zbl: 0938.37025
and ,[LM] Horseshoes, entropy and periods for graph maps, Topology, 32 (1993), 649-664. | MR: 94k:58113 | Zbl: 0787.54021
and ,[LPR1] The full periodicity kernel for σ maps, J. Math. Anal. and Appl., 182 (1994), 639-651. | MR: 95c:58142 | Zbl: 0807.58039
, and ,[LPR2] Sets of periods for maps on connected graphs with zero Euler characteristic having all branching points fixed, to appear in J. Math. Anal. and Appl. | MR: 1719076 | Zbl: 0965.37035
, and ,[LPR3] International Journal of Bifurcation and Chaos, 5 (1995), 1395-1405. | Zbl: 0886.58028
, and ,[LR] Sur le nombre d'orbites périodiques d'une application continue du cercle en lui-même, C. R. Acad. Sci. Paris, Sér. I Math., 294 (1982), 52-54. | MR: 651074 | Zbl: 0477.54023
and ,[LY] Period three implies chaos, Amer. Math. Monthly, 82 (1975), 985-992. | MR: 52 #5898 | Zbl: 0351.92021
and ,[M] Periodes 1, 2, 3, 4, 5, 7 equivalen a caos, Master Thesis, Universitat Autònoma de Barcelona, 1982.
,[Sh] Co-existence of the cycles of a continuous mapping of the line into itself (Russian), Ukrain. Math. Zh., 16 (1964), 61-71. | MR: 159905
,[St] Periodic points of continuous functions, Math. Mag., 51 (1978), 99-105. | MR: 80h:58043 | Zbl: 0455.58022
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