Abstract
We prove that every generic three-dimensional flow has either infinitely many sinks or finitely many sectional-hyperbolic attractors whose basins form a full Lebesgue measure set. In particular, all such flows exhibit sectional-hyperbolic attractors.
Funding Statement
Work partially supported by MATHAMSUB 15 MATH05-ERGOPTIM, Ergodic Optimization of Lyapunov Exponents.
Acknowledgments
The author thanks professors A. Arbieto, S. Bautista and B. Santiago for helpful conversations. He also thanks some anonymous referees concerning Theorem 2.4 and the proof of Lemma 3.5.
Citation
C.A. Morales. "Existence of sectional-hyperbolic attractors for three-dimensional flows." SUT J. Math. 51 (2) 227 - 249, December 2015. https://doi.org/10.55937/sut/1454685868
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