Author

E. Shelukhin

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Preprint Oct 2026

Invariant sets and spectral rigidity of Hamiltonian diffeomorphisms

We solve a well-known question of Polterovich from 2002 regarding the rigidity of Hamiltonian diffeomorphisms in Hofer's metric in dimension two: every non-trivial Hamiltonian diffeomorphism of a surface of genus at least one has all positive iterations separated from the identity in Hofer's metric. In higher dimension...

Habib Alizadeh, E. Shelukhin · 0 citations

Preprint Aug 2026

A proof of the Arnold-Givental conjecture

We prove the Arnold-Givental conjecture in full generality: given a closed symplectic manifold $(X, \omega)$, an anti-symplectic involution $\tau_X: X \to X$ with fixed point set $L={\rm Fix}(\tau_X)$, and a Hamiltonian diffeomorphism $\phi: X \to X$ such that $\phi(L)$ intersects transversely with $L$, the following i...

Shao-Yun Bai, E. Shelukhin, Yi Wang et al. · 1 citation