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Unstable periodic orbits and semiclassical quantization. (English) Zbl 0655.58039

The Bohr-Sommerfeld quantization condition has a meaningful extension to classical chaotic systems whose periodic (unstable) orbits are isolated. It provides a semiclassical Euler factorization for the functional determinant of the quantal Hamiltonian, in contrast to the Hadamard infinite product over the eigenvalues by which the exact determinant is defined.

MSC:

58Z05 Applications of global analysis to the sciences
37G99 Local and nonlocal bifurcation theory for dynamical systems
53D50 Geometric quantization
81V10 Electromagnetic interaction; quantum electrodynamics
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