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We present a method to obtain a Taylor model representation of the Poincare map from the original Taylor model flow representation. First a high-order polynomial approximation of the time necessary to reach the Poincare section is determined as a function of the initial conditions. This is achieved by reducing the problem to a non-verified polynomial inversion. This approximate crossing time is inserted into the Taylor model of the time-dependent flow, leading to an approximate Poincare map. A verified correction is performed heuristically which provides a rigorous enclosure of the Poincare map given, demonstrating achieved accuracy with verification.
J. Grote, K. Makino, M. Berz, Transactions on Systems 11,4 (2005) 1986-1992
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