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Continued fractals and the Seifert conjecture
Author(s):
Jenny
Harrison
Journal:
Bull. Amer. Math. Soc.
13
(1985),
147-153.
MSC (1980):
Primary 58F25, 34C35, 10K10
MathSciNet review:
799799
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Additional information
References:
- [AR] R. Abraham and J. Robbin, Transversal mappings and flows, Benjamin, New York, 1967. MR 240836
- [Ah] L. V. Ahlfors, Lectures on quasi-conformal mappings, Van Nostrand, Princeton, N.J., 1966. MR 200442
- [D] A. Denjoy, Sur les courbes definies par les équations differentielles à la surface du tore, J. Math. Pures Appl. 11 (1932), 333-375.
- [Ha] G. R. Hall, A C, Ergodic Theory and Dynamical Systems, Vol. 1 (1981), 261-272. MR 662469
- [H1] J. Harrison, Denjoy fractals, (preprint). MR 991099
- [H2] J. Harrison, C, (preprint).
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- [H4] J. Harrison, Topological transitivity for Ahlfors quasi-circles, (preprint).
- [H5] J. Harrison, Bounded distortion and an n-dimensional Denjoy Theorem (in preparation).
- [H6] J. Harrison, Diophantine type and the Denjoy-Koksma inequality, (in preparation).
- [HN1] J. Harrison and A. Norton, An improved sampling procedure for the uniform distribution of na, (preprint).
- [HN2] J. Harrison and A. Norton, Denjoy quasi-circles in R with Hausdorff dimension n ― ε (in preparation).
- [HY] J. Harrison and J. A. Yorke, Vector fields on S3 and R3 without periodic-points, Proc. Simposio Internac. de Sistemas Dinamicos, Springer Lecture Notes.
- [Ht] D. Hart, On the smoothness of generators, Topology 22 (1983), 357-363. MR 710109
- [He] M. Herman, Contre-exemples de Denjoy et contre-exemples de classe C, (preprint).
- [Kh] A. Khintchine, Continued fractions, translated by P. Wynn (1963) Groningen, Nordhoff. MR 161834
- [Kn] R. J. Knill, A C3 with a Denjoy minimal set, J. Differential Geom. 16 (1981), 271-280. MR 638792
- [KN] L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley, New York, 1974. MR 419394
- [M] J. Mather, Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, (preprint).
- [N] A. Norton, A critical set with non-null image has large Hausdorff dimension, (preprint).
- [P] C. Pugh, The Closing Lemma, Amer. J. Math. 89 (1967), 956-1021. MR 226669
- [Sch] P. Schweitzer, Counterexamples to the Seifert conjecture and opening closed leaves of foliations, Ann. of Math. (2) 100 (1971), 386-400. MR 356086
- [Sei] H. Seifert, Closed integral curves in 3-space and isotopic two-dimensional deformations, Proc. Amer. Math. Soc. 1 (1950), 287-302. MR 37508
- [W] H. Whitney, Analytic extensions of differentiable functions defined on closed sets, Trans. Amer. Math. Soc. 36 (1934), 369-387. MR 1501749
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Additional Information:
DOI:
10.1090/S0273-0979-1985-15400-X
PII:
S 0273-0979(1985)15400-X
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