{"product_id":"topics-in-modern-mathematics-petrovskii-seminar-von-o-oleinik-hrsg","title":"Topics in Modern Mathematics","description":"\u003cp\u003e1.1. 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 \u0026gt; 0 are given l.n Sec. 4 [IJ.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9781468416558\"\u003e\u003ch3\u003ePetrovskii Seminar\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9781468416558","offer_id":39416966840413,"sku":"9781468416558","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/5e091659-da9a-4898-a02d-c281a5fca428.jpg?v=1774757483","url":"https:\/\/shop.autorenwelt.de\/en\/products\/topics-in-modern-mathematics-petrovskii-seminar-von-o-oleinik-hrsg","provider":"Autorenwelt Shop","version":"1.0","type":"link"}