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Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor |
ALI M., SAHA L.M. |
Department of Mathematics, Faculty of Mathematical Science, Delhi University, Delhi 110007, India; Department of Mathematics, Zakir Husain College, Delhi University, New Delhi 110002, India |
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Abstract A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring trajectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent |?1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (|?1>0) or not (|?1?ü0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate |?1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.
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Received: 12 August 2004
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