DOI: 10.1017/s0143385700001371. A relation between Lyapunov exponents, Hausdorff dimension and entropy

A relation between Lyapunov exponents, Hausdorff dimension and entropy

10.1017/s0143385700001371

Crossref journal-article

Cambridge University Press (CUP)

Ergodic Theory and Dynamical Systems (56)

Abstract

AbstractFor an Axiom A diffeomorphism of a surface with an ergodic invariant measure we prove that the entropy is the product of the positive Lyapunov exponent and the Hausdorff dimension of the set of generic points in an unstable manifold.

Bibliography

Manning, A. (1981). A relation between Lyapunov exponents, Hausdorff dimension and entropy. Ergodic Theory and Dynamical Systems, 1(4), 451â459.

Authors 1

Anthony Manning (first)

References 22 Referenced 54

10.1070/RM1977v032n04ABEH001639
{'key': 'S0143385700001371_ref001', 'article-title': 'Topological entropy and equivalence of dynamical systems', 'volume': '219', 'author': 'Adler', 'year': '1979', 'journal-title': 'Mem. Amer. Math. Soc.'} / Mem. Amer. Math. Soc. / Topological entropy and equivalence of dynamical systems by Adler (1979)
10.1090/S0002-9947-1973-0338317-X
{'key': 'S0143385700001371_ref003', 'volume-title': 'Lecture Notes in Maths.', 'author': 'Bowen', 'year': '1975'} / Lecture Notes in Maths. by Bowen (1975)
10.1090/pspum/014/0271990
10.1007/BF02684767
10.1007/BF01389848
10.1007/BF02684768
10.1070/RM1972v027n04ABEH001383
10.1090/pspum/014/0271991
10.1007/BF02684777
[14] McCluskey H. & Manning A. . Hausdorff dimension for horseshoes. In preparation.
{'key': 'S0143385700001371_ref006', 'volume-title': 'Lecture Notes in Maths.', 'author': 'Denker', 'year': '1976'} / Lecture Notes in Maths. by Denker (1976)
10.1007/BF01692494
10.1007/BF02584795
{'key': 'S0143385700001371_ref015', 'volume-title': 'Differentiable Dynamics', 'author': 'Nitecki', 'year': '1971'} / Differentiable Dynamics by Nitecki (1971)
[13] Ledrappier F. . Some relations between dimension and Lyapunov exponents. Preprint. CNRS, 1981. (10.1007/BF01208896)
10.1016/0022-0396(76)90004-8
{'key': 'S0143385700001371_ref011', 'volume-title': 'Dimension Theory', 'author': 'Hurewicz', 'year': '1941'} / Dimension Theory by Hurewicz (1941)
10.1090/S0002-9904-1967-11798-1
10.1070/IM1971v005n02ABEH001050
10.1070/IM1976v010n06ABEH001835

Dates

Type	When
Created	16 years, 11 months ago (Sept. 19, 2008, 7:23 a.m.)
Deposited	6 years, 3 months ago (May 25, 2019, 11:16 a.m.)
Indexed	1 month, 2 weeks ago (July 11, 2025, 6:28 a.m.)
Issued	43 years, 8 months ago (Dec. 1, 1981)
Published	43 years, 8 months ago (Dec. 1, 1981)
Published Online	16 years, 11 months ago (Sept. 19, 2008)
Published Print	43 years, 8 months ago (Dec. 1, 1981)

Funders 0

None

BibTeX

@article{Manning_1981, title={A relation between Lyapunov exponents, Hausdorff dimension and entropy}, volume={1}, ISSN={1469-4417}, url={http://dx.doi.org/10.1017/s0143385700001371}, DOI={10.1017/s0143385700001371}, number={4}, journal={Ergodic Theory and Dynamical Systems}, publisher={Cambridge University Press (CUP)}, author={Manning, Anthony}, year={1981}, month=dec, pages={451–459} }

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