31,085 research outputs found
Symplectic Regularization of Binary Collisions in the Circular N+2 Sitnikov Problem
We present a brief overview of the regularizing transformations of the Kepler
problem and we relate the Euler transformation with the symplectic structure of
the phase space of the N-body problem. We show that any particular solution of
the N-body problem where two bodies have rectilinear dynamics can be
regularized by a linear symplectic transformation and the inclusion of the
Euler transformation into the group of symplectic local diffeomorphisms over
the phase space. As an application we regularize a particular configuration of
the circular N+2 Sitnikov problem.Comment: 23 pages, 5 figures. References to algorithmic regularization
included, changes in References and small typographic corrections. Accepted
in J. of Phys. A: Math. Theor 44 (2011) 265204
http://stacks.iop.org/1751-8121/44/26520
Sigma theory for Bredon modules
We develop new invariants similar to the Bieri-Strebel-Neumann-Renz
invariants but in the category of Bredon modules (with respect to the class of
the finite subgroups of G). We prove that for virtually soluble groups of type
FP_{\infty} and finite extension of the Thompson group F the new invariants
coincide with the classical ones
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