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No crossing occur !!! Lorenz system has chaotic solution. > Nonlinearity: the two nonlinearities are xy and xz -> Symmetry: (x, y) -> (-x, -y)Ģ8 Lorenz attractor -> Fixed points:  stable point forĢ9 Lorenz attractor -> Fixed points:  stable point forģ0 Lorenz attractor -> Fixed points:  stable point forģ1 Lorenz attractor -> Fixed points:  stable point forģ2 Lorenz attractor  Unstable points forģ3 Lorenz attractor  Unstable points for cģ4 Lorenz attractor  Unstable points forģ5 Lorenz attractor No crossing occur !!!ģ6 Lorenz attractor No crossing occur !!! Strange attractorģ7 Lorenz attractor Lorenz system has chaotic solution. > Poincaré sections -> Lyapunov exponent Chaos in general relativity Chaos in Lifshitz spacetimes -> motivation Conclusion Fractal Future direction with the motivation It was hidden ! -> chaosmos (chaos + cosmos) Can we describe this in the field theoretical viewpoint with continuous symmetry ? 19Ģ1 Contents Motivation What is chaos? Measuring chaos It was hidden ! -> chaosmos (chaos + cosmos) 18ġ9 Motivation -> chaosmos (chaos + cosmos) This is scale symmetry !

Presentation on theme: "Chaos in general relativity"- Presentation transcript:ġ4 Motivation This is scale symmetry ! It was hidden ! 14ġ5 Motivation This is scale symmetry ! It was hidden ! 15ġ6 Motivation This is scale symmetry ! It was hidden ! 16ġ7 Motivation This is scale symmetry ! It was hidden ! 17ġ8 Motivation -> chaosmos (chaos + cosmos) This is scale symmetry !