Vol.1, No 4, 1997 pp. 21 - 27
UDC: 530.1.145

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EQUIVALENT CRITICAL BEHAVIOUR OF THE PERIODIC HAMILTONIAN MAPS
N. Burić^1,2, M. Mudrinić² , K. Todorović^1
1Department of Physics and Mathematics, Faculty of Pharmacy, Vojvode Stepe450, Beograd, Yugoslavia
e-mail: majab@rudjer.ff.bg.ac.yu
²Institute of Physics, PO Box 57, Beograd, Yugoslavia
e-mail: mudrinic@shiva.phy.bg.ac.yu

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Abstract. Recently we have shown that the fractal properties of the critical invariant circles of the standard-map, as summarised by the f(alpha) spectrum and the generalised dimensions D(q), depend only on the tails in the continued fraction expansion of the corresponding rotation numbers [1]. In this paper this result is extended on the whall class of 2pi-periodic area-preserving maps. We present numerical evidence that the f(alpha) and D(q) are the same for all critical invariant circles of any such map which have the rotation numbers with the same tail.

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EKVIVALENTNE KLASE PONAŠANJA PERIODIČNIH HAMILTONOVIH PRESLIKAVANJA Nedavno smo pokazali da fraktalne osobine kritičnih invarijantnih krugova standardnog preslikavanja, opisane f(alpha) spektrom i spektrom generalisanih dimenzija D(q), zavise samo od repa u verižnom razlomku odgovarajućeg rotacionog broja [1]. U ovom članku je taj rezultat proširen na čitavu klasu 2pi-periodičnih preslikavanja koja očuvavaju površinu. Dati su numerički rezultati koji potvrđuju da su f(alpha) i D(q) isti za sve kritične invarijantne krugove ma kog takvog preslikavanja ukoliko imaju isti rep u verižnom razlomku rotacionog broja.