Abstract
We calculate the Hörmander index in the finite-dimensional case. Then we use the result to give some iteration inequalities, and prove almost existence of mean indices for given complete autonomous Hamiltonian system on compact symplectic manifold with symplectic trivial tangent bundle and given autonomous Hamiltonian system on regular compact energy hypersurface of symplectic manifold with symplectic trivial tangent bundle.
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Acknowledgements
The authors would like to thank the referees for their critical reading and very helpful comments and suggestions. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11221091, 11471169) and LPMC of MOE of China.
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Zhou, Y., Wu, L. & Zhu, C. Hörmander index in finite-dimensional case. Front. Math. China 13, 725–761 (2018). https://doi.org/10.1007/s11464-018-0702-3
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DOI: https://doi.org/10.1007/s11464-018-0702-3