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Bifurcations and foliations of the Kovalevskaya System Peter H. Richter - Institut für Theoretische Physik International Conference Classical Problems of Rigid Body Dynamics Donetsk, June 23-25, 2004

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Survey Peter H. Richter - Institut für Theoretische Physik Mathematical vs. physical definition Equations and constants of motion Analysis: VB program –Kovalevskaya, Kötter, Zhukovsky, Appelrot Topology: IWF video –Kharlamov, Fomenko, Oshemkov, Bolsinov Physics: –Periods, actions

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Peter H. Richter - Institut für Theoretische Physik Equations of motion and integrals Euler-Poisson equations Poisson sphere radius angular momentum energy Kovalevskaya constant first integrals

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Solving the equations Peter H. Richter - Institut für Theoretische Physik VB

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The amazing richness of the Kovalevskaya System Peter H. Richter - Institut für Theoretische Physik 4 topologically different (h,l)-level sets 4 Appelrot classes of critical tori with 2+2+4+7 subclasses 5 Liouville families of invariant tori 5 Kharlamov types of foliations 10 kinds of Poincaré surfaces of section 10 types of iso-energy surfaces h=const

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Poincaré surfaces of section Peter H. Richter - Institut für Theoretische Physik A B C C0C0 S 3 S 2 D D0D0 E E H RP 3 T 2 I K 3 3S 2 G F F S 1 xS 2 2S 2

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Fomenko stacks Peter H. Richter - Institut für Theoretische Physik - 0.50.91.21.451.7 1.81.92.34.09.0

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Periods and Actions Peter H. Richter - Institut für Theoretische Physik periods H flow K flow actions DRV1998

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Action representation of iso-energy surfaces Peter H. Richter - Institut für Theoretische Physik - 0.5 0.91.2 1.452.39.0

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Acknowledgements Peter H. Richter - Institut für Theoretische Physik Andreas Wittek Maria Juhnke Emil Horosov Holger R. Dullin Mikhail P. Kharlamov Alexey V. Bolsinov Igor Gashenenko Alexander P. Veselov

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