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Abstract: Some universal aspects of weak chaos are discussed by using two types of non-hyperbolic dynamics; intermittent chaos and hamiltonian chaos. First, several characteristic quantities which describe the non-stationarity of strong intermittency are reviewed by use of the modified Bernoulli map. The statistical features of weak chaos are described in the framework of the renewal theory as well as the infnite measure ergodic theory. Secondly, we discuss the slow dynamics in generic hamiltonian systems, where the slow dyanmics called "Arnold diffusion" appears in very narrow stagnant layers between KAM invariant tori and chaos. The Nekhoroshev's characteristic time enables us to derive the statistical distribution obeying the Log-Weibull distribution function. One can see that the universal distribution is observed in the numerical simulations. Here I will introduce two numerical results for high-dimensional hamiltonian dynamics; one is the cluster formation and another is the FPU lattice vibration. Finally, I will introduce the recent developement in our group concerning the infinite measure ergodicity in dissipative dynamics.
Seminarsko predavanje bo v četrtek 15. maja 2014 ob 15:15 uri v seminarski sobi CAMTP na Krekovi 2, pritličje desno. Vljudno vabljeni vsi zainteresirani, tudi študentje.