Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/144297
Title: Interpolating vector fields for near indentity maps and averaging
Author: Gelfreich, V.
Vieiro Yanes, Arturo
Keywords: Interpolació (Matemàtica)
Camps vectorials
Interpolation
Vector fields
Issue Date: 2-Aug-2018
Publisher: IOP Publishing
Abstract: For a smooth near identity map, we introduce the notion of an interpolating vector field written in terms of iterates of the map. Our construction is based on Lagrangian interpolation and provides an explicit expression for autonomous vector fields which approximately interpolate the map. We study properties of the interpolating vector fields and explore their applications to the study of dynamics. In particular, we construct adiabatic invariants for symplectic near identity maps. We also introduce the notion of a Poincaré section for a near identity map and use it to visualise dynamics of four-dimensional maps. We illustrate our theory with several examples, including the Chirikov standard map, a volume-preserving map and a symplectic map in dimension four. The last example is motivated by the theory of Arnold diffusion.
Note: Versió postprint del document publicat a: https://doi.org/10.1088/1361-6544/aacb8e
It is part of: Nonlinearity, 2018, vol. 31, num. 9
URI: http://hdl.handle.net/2445/144297
Related resource: https://doi.org/10.1088/1361-6544/aacb8e
ISSN: 0951-7715
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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