Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces

We define Floer homology for a time-independent, or autonomous Hamiltonian on a symplectic manifold with contact type boundary, under the assumption that its 1-periodic orbits are transversally nondegenerate. Our construction is based on Morse-Bott techniques for Floer trajectories. Our main motivation is to understand the relationship between linearized contact homology of a fillable contact manifold and symplectic homology of its filling.
Comment: Final version, 92 pages, 7 figures, index of notations. Remark 4.9 in Version 1 is wrong. To correct it we modified the weights for the Sobolev spaces along the gradient trajectories (Figure 3). Proposition 4.8 in Version 1 is now split into Propositions 4.8 and 4.9. This version contains full details for the second derivative estimates in Lemma 4.20