MathDBPalis's conjecture on Morse–Smale systems and transversal homoclinic orbits
Palis's conjecture on Morse–Smale systems and transversal homoclinic orbits
A diffeomorphism is a diffeomorphism of a compact manifold. Palis's conjecture. Any diffeomorphism can be approximated by a Morse–Smale one or by one exhibiting a transversal homoclinic orbit. This conjecture proposes a fundamental dichotomy between simple Morse–Smale dynamics and dynamics with transversal homoclinic complexity; its status is not specified in the source.
Sources & referencesView supporting material
Primary source
Gang Liao and Jing Wei, “Metric entropy and homoclinic growth rate”, arXiv:2511.08227 (2025).
Additional references
13 papers in this index state this conjecture (2004–2025). The statement above is taken from the most recent of them; the others are arXiv:1806.09011, arXiv:1506.07221, arXiv:1410.1758, arXiv:1404.5130, arXiv:1403.6050, arXiv:1103.0869, arXiv:1011.3836, arXiv:1011.2935, arXiv:1004.2893, arXiv:0809.4965, arXiv:math/0605387, arXiv:nlin/0408011.
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