Strong transitivity and graph maps

• Autorzy: Yokoi K.

Identyfikatory

DOI

10.4064/ba53-4-3

• Języki publikacji: EN

Abstrakty

EN

We study the relation between transitivity and strong transitivity, introduced by W. Parry, for graph self-maps. We establish that if a graph self-map f is transitive and the set of fixed points of f^k is finite for each k ≥ 1, then f is strongly transitive. As a corollary, if a piecewise monotone graph self-map is transitive, then it is strongly transitive.

Słowa kluczowe

EN

transitive; strongly transitive; graph

PL

graf

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 4
• Strony: 377--388
• Opis fizyczny: Bibliogr. 9 poz., wykr.

Twórcy

autor

Yokoi K.

• Department of Mathematics, Shimane University, Matsue, 690-8504, Japan,

Bibliografia

• [1] Ll. Alsedà, M. A. del Rio, and J. A. Rodriguez, A splitting theorem for transitive maps, J. Math. Anal. Appl. 232 (1999), 359-375.
• [2] M. Barge and J. Martin, Chaos, periodicity, and snakelike continua, Trans. Amer. Math. Soc. 289 (1985), 355-365.
• [3] —, —, Dense orbits on the interval, Michigan Math. J. 34 (1987), 3-11.
• [4] A. M. Blokh, On transitive mappings of one-dimensional branched manifolds, in: Differential-Difference Equations and Problems of Mathematical Physics, Akad. Nauk Ukrain. SSR, Inst. Mat. Kiev, 1984, 3-9, 131 (in Russian).
• [5] —, The connection between entropy and transitivity for one-dimensional mappings, Uspekhi Mat. Nauk 42 (1987), no. 5, 209-210 (in Russian).
• [6] E. M. Coven and I. Mulvey, Transitivity and the centre for maps of the circle, Ergodic Theory Dynam. Systems 6 (1986), 1-8.
• [7] W. Parry, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc. 122 (1966), 368-378.
• [8] R. P. Roe, Dynamics and indecomposable inverse limit spaces of maps on finite graphs, Topology Appl. 50 (1993), 117-128.
• [9] —, Dense periodicity on finite trees, Topology Proc. 19 (1994), 237-248.