In this paper, we study local structures of volume-preserving maps and source-free vector fields, which are defined in the Euclidean n-space R-n with n >= 3. First, we prove that any volume-preserving map, defined in some neighbourhood of the origin, can be represented as a composition of n - 1 essentially two-dimensional area-preserving maps. This result can be viewed as an analogue of the following known fact (Feng and Shang 1995 Volume-preserving algorithms for source-free dynamical systems Numer. Math. 71 451-63): any source-free vector field on R-n can be represented as a sum of n - 1 essentially two-dimensional Hamiltonian vector fields. Then, we present a local representation of source-free vector fields under volume-preserving coordinate changes. Finally, we construct a Lie algebra of skew-symmetric tensor potentials of second order associated with source-free vector fields. The Lie algebra turns out to be isomorphic to the Lie algebra of source-free vector fields.
Chinese Acad Sci, Inst Math Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714
Shang, ZJ. Volume-preserving maps, source-free systems and their local structures[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL,2006,39(19):5601-5615.
APA
Shang, ZJ.(2006).Volume-preserving maps, source-free systems and their local structures.JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL,39(19),5601-5615.
MLA
Shang, ZJ."Volume-preserving maps, source-free systems and their local structures".JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 39.19(2006):5601-5615.
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