A transitive map on [0,1] whose inverse limit is the pseudoarc

A transitive map on $[0,1]$ whose inverse limit is the pseudoarc
HTML articles powered by AMS MathViewer

Proc. Amer. Math. Soc. 111 (1991), 1165-1170

DOI: https://doi.org/10.1090/S0002-9939-1991-1042271-1

PDF | Request permission

We construct a transitive map on $[0,1]$ so that the inverse limit of copies of $[0,1]$ with $f$ as the bonding map is a pseudoarc.

References

Marcy Barge and Judy Kennedy, Continuum theory and topological dynamics, Open problems in topology, North-Holland, Amsterdam, 1990, pp. 633–644. MR 1078669
Marcy Barge and Joe Martin, Chaos, periodicity, and snakelike continua, Trans. Amer. Math. Soc. 289 (1985), no. 1, 355–365. MR 779069, DOI 10.1090/S0002-9947-1985-0779069-7
Marcy Barge and Joe Martin, Dense orbits on the interval, Michigan Math. J. 34 (1987), no. 1, 3–11. MR 873014, DOI 10.1307/mmj/1029003477
Marcy Barge and Joe Martin, The construction of global attractors, Proc. Amer. Math. Soc. 110 (1990), no. 2, 523–525. MR 1023342, DOI 10.1090/S0002-9939-1990-1023342-1
R. H. Bing, A homogeneous indecomposable plane continuum, Duke Math. J. 15 (1948), 729–742. MR 27144
R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653–663. MR 43450
George W. Henderson, The pseudo-arc as an inverse limit with one binding map, Duke Math. J. 31 (1964), 421–425. MR 166766
M. Hénon, A two-dimensional mapping with a strange attractor, Comm. Math. Phys. 50 (1976), no. 1, 69–77. MR 422932
Judy Kennedy, A transitive homeomorphism on the pseudoarc which is semiconjugate to the tent map, Trans. Amer. Math. Soc. 326 (1991), no. 2, 773–793. MR 1010412, DOI 10.1090/S0002-9947-1991-1010412-2

Un continu dont tout sous-continu est indécomposable

3

Edwin E. Moise, An indecomposable plane continuum which is homeomorphic to each of its nondegenerate subcontinua, Trans. Amer. Math. Soc. 63 (1948), 581–594. MR 25733, DOI 10.1090/S0002-9947-1948-0025733-4