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Weakly noisy chaotic scattering.

Juan D Bernal1, Jesús M Seoane, Miguel A F Sanjuán

  • 1Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.

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Summary
This summary is machine-generated.

Weak Gaussian noise can slow particle escape in chaotic scattering systems, altering dynamics and topology. Noise reduces fractal basin boundaries, impacting phase space structure and long transient behaviors.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Chaotic scattering is crucial in various physical systems.
  • Understanding noise effects on chaotic dynamics is essential.
  • The Hénon-Heiles Hamiltonian system provides a paradigmatic model for open, nonhyperbolic chaos.

Purpose of the Study:

  • To investigate the impact of weak additive uncorrelated Gaussian noise on chaotic scattering dynamics and topology.
  • To analyze the effects of noise on time escape distributions and survival probability.
  • To examine changes in phase space basin structure under the influence of noise.

Main Methods:

  • Simulations of the Hénon-Heiles Hamiltonian system with additive Gaussian noise.
  • Analysis of time escape distributions and survival probability as a function of noise intensity.
  • Computation of exit basins in phase space to study topological changes.

Main Results:

  • Long transients observed in time escape distributions at critical noise intensities, leading to slower particle escape.
  • Survival probability exhibits a smooth curve with a local maximum and minimum, correlating with transients and basin structure.
  • Noise reduces the fractal nature of basin boundaries, resulting in a quadratic curve for exit basins.

Conclusions:

  • Weak Gaussian noise significantly influences the dynamics and topology of chaotic scattering.
  • Noise can induce slower escape rates and alter the complex fractal structures of phase space basins.
  • The study reveals a transition from fractal to non-fractal basin boundaries with increasing noise intensity.