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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.11445 |
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Table of Contents:
- We show that the eigenfunctions of the self-adjoint elliptic $h-$differential operator $P_{h}(t)$ exhibits semiclassical scar phenomena on the $d-$dimensional torus, under the $σ$-Bruno-Rüssmann condition, instead of the Diophantine one. Its equivalence is described as: for almost all perturbed Hamiltonian's KAM Lagrangian tori $Λ_ω$, there exists a semiclassical measure with positive mass on $Λ_ω$. The premise is that we can obatain a family of quasimodes for the $h-$differential operator $P_{h}(t)$ in the semiclassical limit as $h\rightarrow0$, under the $σ$-Bruno-Rüssmann condition.