کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1896381 1044427 2011 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Continuous symmetry reduction and return maps for high-dimensional flows
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Continuous symmetry reduction and return maps for high-dimensional flows
چکیده انگلیسی

We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetry-equivalent points is represented by a single point. In either approach, numerical computations can be performed in the original state space representation, and the solutions are then projected onto the symmetry-reduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a five-dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for high-dimensional flows, symmetry reduction by the method of moving frames offers hope.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 240, Issue 2, 15 January 2011, Pages 187–198
نویسندگان
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