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Resonance and fractal geometry

Resonance and fractal geometry

Conclusions

Conclusions Ico-existence periodicity (including resonance),quasi-periodicity and chaosin product state- and parameter spacebifurcations (phase transitions): singularitiesnon-resonances: Kolmogorov-Arnol ′ d-Moser theoryH.W. Broer, KAM theory: the legacy of Kolmogorov’s 1954 paper. Bull. AMS (New Series) 41(4)(2004) 507-521H.W. Broer, H. Hanßmann and F.O.O. Wagener, Quasi-Periodic Bifurcation Theory, the geometryof KAM. (Monograph in preparation)

Conclusions IIfractal geometry with infinite regressnowhere dense −→ meagremodelling at larger scaleD. Ruelle and F. Takens, On the nature of turbulence. Comm. Math. Phys. 20 (1971) 167-192;23 (1971) 343-344H.W. Broer, B. Hasselblatt and F. Takens (eds.): Handbook of Dynamical Systems. Volume 3North-Holland (2010)

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