Geometric results for hyperbolic operators with spectral transition of the Hamilton map

2025/05/27 by Enrico Bernardi, Tatsuo Nishitani, Bernardi, Enrico +1 · 1 citation
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #advanced mathematical theories #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2505.21078

Abstract

In this paper we study a class of non-effectively hyperbolic operators vanishing of order 2 on a manifold, on a sub-region of which the spectral structure of the Hamilton map changes type. Suitable normal symplectic coordinates are found together with an analysis of the Hamilton system associated to the principal symbol and a factorization result, preparing the operator for a microlocal energy estimate, is finally proven.

Citations

• On the Cauchy problem for non-effectively hyperbolic operators, the Gevrey 5 well-posedness
• The Cauchy problem for differential equations with double characteristics

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