Abstract
We prove that every \(C^1\) three-dimensional flow with positive topological entropy can be \(C^1\) approximated by flows with homoclinic orbits.
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Acknowledgements
Funding was provided by CNPq (Grant No. 303389/2015-0) and MATHAMSUB 15 MATH05-ERGOPTIM, Ergodic Optimization of Lyapunov Exponents.
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Partially supported by MATHAMSUB 15 MATH05-ERGOPTIM, Ergodic Optimization of Lyapunov Exponents.
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Lopez, A.M., Metzger, R.J. & Morales, C.A. Homoclinic Orbits and Entropy for Three-Dimensional Flows. J Dyn Diff Equat 30, 799–805 (2018). https://doi.org/10.1007/s10884-017-9579-1
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DOI: https://doi.org/10.1007/s10884-017-9579-1