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首都大学東京 非線形物理研究室の吉田 賢典と申します．
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日時：5月22日（月）15時から
場所：首都大学東京 南大沢キャンパス 8号館 308号室
講演者：Jizhou Li 氏 （ワシントン州立大学）
講演題目：Homoclinic decomposition of unstable periodic orbits in chaotic systems
講演概要：
Semiclassical sum rules, such as the Gutzwiller trace formula, depend on the properties of closed (periodic or homoclinic/heteroclinic) orbits. The interferences between such orbit sums are governed by classical action functions and Maslov indices. We investigate the periodic orbits inside the convergence zone of the normal form transformation, which arise from intersections of Moser invariant curves, topologically forced by homoclinic intersections between the stable and unstable manifolds. We show that a rotary-N periodic orbit can be treated in two ways: the first is to identify it as self-intersections of a single Moser curve, forced by a rotary-N (therefore non-primary) homoclinic orbit segment; the second is to identify it as mutual-intersections between N Moser curves, forced by N rotary-1 (primary) homoclinic orbit segments. In both cases, the periodic orbit actions are determined by the corresponding homoclinic actions and certain phase space areas bounded the stable and unstable manifolds. Applications to determine the small action dierences between orbits in cycle expansions are developed as examples of the use and power of these relations.
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首都大学東京 非線形物理研究室
吉田 賢典
yoshida-kensuke[at]ed.tmu.ac.jp