Poincare Analyticity and the Complete Variational Equations

Autor:	Kaltchev, Dobrin, Dragt, Alex
Rok vydání:	2011
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs Mathematics - Dynamical Systems Physics - Accelerator Physics
Druh dokumentu:	Working Paper
DOI:	10.1016/j.physd.2012.08.010
Popis:	According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters providing the right sides of the differential equations are analytic in the variables, the time, and the parameters. We describe how these Taylor expansions may be obtained, to any desired order, by integration of what we call the complete variational equations. As illustrated in a Duffing equation stroboscopic map example, these Taylor expansions, truncated at an appropriate order thereby providing polynomial approximations, can well reproduce the behavior (including infinite period doubling cascades and strange attractors) of the solutions of the underlying differential equations. Comment: 86 pages including 22 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1102.3394 Zobrazit plný text záznamu View this record from Arxiv