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Beyond the Periodic Orbit Theory (1996)
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@MISC{Cvitanovic96beyondthe,
author = {Predrag Cvitanovic and Kim Hansen and Juri Rolf and Gábor Vattay and Vattay Z},
title = {Beyond the Periodic Orbit Theory},
year = {1996}
}
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Abstract
. The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory approach to determining eigenspectra of transfer operators. PACS numbers: 0320, 0365, 0545 AMS classification scheme numbers: 58F20 Dedicated to Adrian Douady for his 60th birthday 1. Introduction Low dimensional chaotic classical and quantum dynamical systems [1, 2] can be analyzed in terms of unstable periodic orbits. The periodic orbit theory of such systems has been successfully applied to a wide range of physical problems [3, 4, 5]. However, since the phase space is tessellated into linearized neighbourhoods of periodic points, analyticity properties of smooth flows are not fully utilized in ...
Keyphrases
periodic orbit theory smooth flow quantum dynamical system adrian douady wide range associated fredholm determinant derive infinite family unstable periodic orbit individual periodic orbit transfer operator conventional periodic orbit theory approach am classification scheme number global constraint 60th birthday physical problem chaotic dynamic introduction low periodic point exact sum rule analyticity property phase space several simple dynamical system pac number linearized neighbourhood simple polynomial form
