By Siceloff L.P., Wentworth G., Smith D.E.
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Peixoto, ‘On an approximation theorem of Kupka and Smale’, J. Diﬀerential Equations 3 (1967) 214–227. 22. D. B. Ray and I. M. Singer, ‘R-torsion and the Laplacian on Riemannian manifolds’, Adv. Math. 7 (1971) 145–210. 23. M. Schwarz, Morse homology, Progress in Mathematics 111 (Birkh¨a user, Basel, 1993). 24. S. Smale, ‘Stable manifolds for diﬀerential equations and diﬀeomorphisms’, Ann. Sc. Norm. Super. Pisa Cl. Sci. 17 (1963) 97–116. DYNAMICS, LAPLACE TRANSFORM AND SPECTRAL GEOMETRY 151 25. V.
Burghelea and S. Haller, ‘Euler structures, the variety of representations and the Milnor–Turaev torsion’, Geom. Topol. 10 (2006) 1185–1238. 6. D. Burghelea and S. Haller, ‘Torsion as a function on the space of representations’, Proceedings of the a user, Basel), to appear. Conference on C ∗ -algebra and elliptic theory II, Trends in Mathematics (Birkh¨ 7. D. Fried, ‘Lefschetz formulas for ﬂows’, Proceedings of the Lefschetz Centennial Conference, Part III, Mexico City, Mexico, 1984, Contemporary Mathematics 58 (American Mathematical Society, Providence, RI, 1987) 19–69.
Assume that Y satisﬁes MS and L. Suppose p∗ ω is Lyapunov for Y where p : W → M denotes the projection. 3, the diﬀerential of the Novikov complex C ∗ (Y ; Λp ∗ ω ) gives rise to a homomorphism of Novikov complexes uY : C ∗ (X− ; Λω ) → C ∗ (X+ ; Λω ). 8) is a quasi-isomorphism. Let s± : X± → X˜± be sections and equip C ∗ (X± ; Λω ) with the corresponding base. Assume that (X− , s− ) and (X+ , s+ ) determine the same Euler structure [5, 25]. 9) x∈X− ˜ → C with dhη = π ∗ η. 8) is ±T (uY ) = ± exp(h∗ PX + − h∗ PX − ) ∈ 1 + Λ+ ω.
Analytical Geometry by Siceloff L.P., Wentworth G., Smith D.E.