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Critical Scaling Behavior near The Accumulation Point

Critical Scaling Behavior near The Accumulation Point. Eui-Sun Lee Department of Physics Kangwon National University. The transition to chaos through an infinite sequence of period-double bifurcation occurs at the accumulation point A ∞. Bifurcation diagram. Parameter Scaling Factor.

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Critical Scaling Behavior near The Accumulation Point

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  1. Critical Scaling Behavior near The Accumulation Point • Eui-Sun Lee • Department of Physics • Kangwon National University The transition to chaos through an infinite sequence of period-double bifurcation occurs at the accumulation point A∞ . Bifurcation diagram

  2. Parameter Scaling Factor Follow the period–doubling bifurcation pointAn of the period – 2n orbit (n=0,1,2,3…) with the stability multiplierλn= -1. An converges to its accumulation point A∞ geometrically with ratio 1/ δ , Define the parameter scaling factor of the level n, as n → ∞ . Converges to and = 4.6692… .

  3. Orbit Scaling Factor Find a period–2n orbit point x n with the maximum distance at A n . converges to its origin point x = 0 geometrically with ratio 1/ α , Define the orbital scaling factor of the level n, and Converges to as n → ∞ . = - 2.5029… .

  4. Parameter and Orbital Scaling Factor Parameter Scaling Factor Orbital Scaling Factor

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