Spectral form factor in the Hadamard-Gutzwiller model: orbit pairs contributing in the third order
Abstract
In this paper we consider orbit pairs contributing in the third order of the spectral form factor in the Hadamard-Gutzwiller model. We prove that periodic orbits including two 2-encounters in certain structures have partner orbits. The action differences are estimated at (1+u1s1)(1+u2s2) with explicit error bounds, where (u1,s1) and (u2,s2) are the coordinates of the piercing points. A new symbolic dynamics for orbit pairs via conjugacy classes is also provided.
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