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- W2111749084 abstract "For many questions in dynamical systems theory it is desirable to have Poincare maps available as a tool to study long-term behavior of the dynamical system under consideration. In a validated setting, the Poincare map should be defined over as large a domain as possible. Taylor model based validated integrators relate final coordinates to initial conditions via a high-order polynomial and a small remainder bound, which usually is many orders of magnitude smaller than the initial domain. It is shown how it is possible to obtain a Taylor model representation of the Poincare map from the original Taylor model flow representation of the ODE. First a high-order polynomial approximation of the time necessary to reach the plane of the Poincare map is determined as a function of the initial conditions. This is achieved by reducing the problem to a non-validated polynomial inversion. This approximate representation is inserted into the Taylor model of the time-dependent flow, leading to an approximate Poincare map. A validated correction is performed that provides a rigorous enclosure of the Poincare map." @default.
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- W2111749084 date "2005-09-15" @default.
- W2111749084 modified "2023-09-23" @default.
- W2111749084 title "High-order validated representation of Poincaré maps" @default.
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