Abstract
There is a general method in ergodic theory which reduces many problems concerning dynamical systems with continuous time to the corresponding problem for dynamical systems with discrete time. This method goes back to Poincaré; for the study of trajectories of a smooth dynamical system in the neighborhood of a closed trajectory he proposed to consider the “return” map which arises on a transversal surface of codimension 1 to the closed trajectory: the transformation consists in following the trajectory starting at a given point of the surface until its next intersection with the surface.
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© 1982 Springer-Verlag New York Inc.
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Cornfeld, I.P., Fomin, S.V., Sinai, Y.G. (1982). Special Representations of Flows. In: Ergodic Theory. Grundlehren der mathematischen Wissenschaften, vol 245. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-6927-5_11
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DOI: https://doi.org/10.1007/978-1-4615-6927-5_11
Publisher Name: Springer, New York, NY
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