Resonance and fractal geometry

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Hopf saddle-node II0.1boxH0.05d10-0.05-0.1O0.2 0.4 0.6 0.8 1 1.2 1.4Id2HH.W. Broer, C. Simó and R. Vitolo, The Hopf-Saddle-Node bifurcation for fixed points of3D-diffeomorphisms, analysis of a resonance ‘bubble’. Physica D 237 (2008) 1773-1799H.W. Broer, C. Simó and R. Vitolo, The Hopf-Saddle-Node bifurcation for fixed points of3D-diffeomorphisms, the Arnol ′ d resonance web. Bull. Belgian Math. Soc. Simon Stevin 15(2008) 769-787H.W. Broer, C. Simó and R. Vitolo, Chaos and quasi-periodicity in diffeomorphisms of the solidtorus. DCDS-B 14(3) (2010) 871-905
Hopf saddle-node III1n=0.46C1C100-1-1 0 1xy-1zx-1 0 11n=0.4555D1D100-1-1 0 1xy-1zx-1 0 1corresponding dynamics: quasi-periodicity and chaos...
Page 1 and 2: Resonance and fractal geometryHenk
Page 3: What is resonance?Resonance: intera
Page 6 and 7: Tidal resonanceMoon ‘caught’ by
Page 8 and 9: Mathematical programmemodelling in
Page 10 and 11: Example: Arnol ′ d familyϕ ↦
Page 12 and 13: Devil’s staircase0.60.4̺0.20-0.2
Page 15: Hopf-Neĭmark-Sacker Imore general:
Page 18 and 19: Conclusions ‘Arnol ′ d’ tongu
Page 20: Resonance tongues swing665544332211
Page 23 and 24: Quasi-periodic Schrödingertongues
Page 25: Hopf saddle-node Imap P : R 3 → R
Page 29: Conclusions IIfractal geometry with

Resonance and fractal geometry

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