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TY - CONF AU - Andrianov, S.N. AU - Zyuzin, D. ED - Petit-Jean-Genaz, Christine ED - Arduini, Gianluigi ED - Michel, Peter ED - Schaa, Volker RW TI - Control of Calculations in the Beam Dynamics using Approximate Invariants J2 - Proc. of IPAC2014, Dresden, Germany, June 15-20, 2014 C1 - Dresden, Germany T2 - International Particle Accelerator Conference T3 - 5 LA - english AB - One of the important problems in the theory of dynamical systems is to find corresponding (invariants). In this article we are discussing some problems of computing of invariant functions (invariants) for dynamical systems. These invariants can be used for describing of particle beams systems. The suggested method is constructive and based on the matrix formalism for Lie algebraic tools. We discuss two types of invariants: kinematic and dynamic. All calculations can be realized in symbolic forms, in particular, kinematic invariants are based on the theory of representations of Lie algebras (in particular, using the Casimir’s operators). For the case of nonlinear kinematic invariants we propose a recursive scheme, which can be implemented in symbolic forms using instruments of computer algebra (for example, such packages as Maple or Mathematica). The corresponding expressions for invariants can be used to control the correctness of computational experiments, first of all for long time beam dynamics. PB - JACoW CP - Geneva, Switzerland SP - 3041 EP - 3043 KW - controls KW - quadrupole KW - experiment KW - emittance KW - database DA - 2014/07 PY - 2014 SN - 978-3-95450-132-8 DO - 10.18429/JACoW-IPAC2014-THPRO071 UR - http://jacow.org/ipac2014/papers/thpro071.pdf ER -