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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Topics in Modern Mathematics: Petrovskii Seminar

Topics in Modern Mathematics: Petrovskii Seminar

Oleinik, O.

Paperback

Series: Contemporary Soviet Mathematics

Gifts & Stationery GeneralGeneral MathematicsGeneral Science

ISBN10: 1468416553
ISBN13: 9781468416558
Publisher: Springer
Published: Nov 17 2012
Pages: 342
Weight: 1.35
Height: 0.74 Width: 7.00 Depth: 10.00
Language: English
1.1. Nearly Integrable Hamiltonian Systems. In this work we examine the system of Hamiltonian equations i = _ iJH, = iJH iJcp iJl with the Hamiltonian function H = Ho(l) ] eH. (I. cp). (1.1) where E: 1 is a small parameter, the perturbation E: Hl (I, cp) is 2n- periodic in CP=CP1,'CPS' and I is an s-dimensional vector, I = Il, --- I s The CPi are called angular variables, and the Ii action variables. A system with a Hamiltonian depending only on the action variables is said to be integrable, and a system with Hamiltonian (1.1) is said to be nearly integrable. The system (1.1) is also called a perturbation of the system with Hamiltonian Ho. The latter system is called un- perturbed. 1.2. An Exponential Estimate of the Time of Stability for the Action Variables. Let I(t), cp(t) be an arbitrary solution of the per- turbed system. We estimate the time interval during which the value I(t) differs slightly from the initial value: II(t)-I(O) I 1. The main result of the work is Theorem 4.4 (the main theorem) which is proved in [1]. This theorem asserts that the above-mentioned interval is estimated by a quantity which grows exponentially as the value of perturbation decreases linearly: 1/(t)-/(O)I 0 and b > 0 are given l.n Sec. 4 [IJ.

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