arXiv subjects

Dobrin Kaltchev

Publications and source records attributed to Dobrin Kaltchev.

2 recordsLinked to original sources

arXiv2012

Convergence of Taylor Transfer Map for Duffing Equation

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 provided that the right sides of the differential equations are analytic in the variables, the time, and the parameters. These Taylor expansions, which provide a transfer map M between initial and final conditions, may be obtained, to any desired order, by integration of the complete variational equations. As an example of this approach, the convergence of such an expansion is investigated for the Duffing equation stroboscopic map in the vicinity of a infinite period doubling cascade and resulting strange attractor.

math-ph↗

arXiv2011

Poincare Analyticity and the Complete Variational Equations

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.

math-ph↗