2 problems

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Avila–Bochi generic conservative Oseledets splitting conjecture
Avila–Bochi conjecture. For a generic conservative diffeomorphism $f\in \operatorname{Diff}^1_m(M)$ , one of the following alternatives holds: all Lyapunov exponents of $f$ are zero…
Conjectureopenconservative-dynamics dynamical-systems oseledets-splittingarXiv posted 2 days ago
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Generic symplectic Oseledets splitting and ergodicity conjecture
Generic symplectic Oseledets splitting conjecture. For a generic $f\in \operatorname{Diff}^1_\omega(M)$ either all Lyapunov exponents vanish almost everywhere, or else the Oseledet…
Conjectureopendynamical-systems oseledets-splitting symplectic-dynamicsarXiv posted 2 days ago

Avila–Bochi generic conservative Oseledets splitting conjecture