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The width of the exponentially narrow stochastic layers
1New York University, Courant Institute of Mathematical Sciences, New York, New York 10012.
Chaos (Woodbury, N.Y.)
|September 1, 1994
Summary
Researchers calculated the exponentially small splitting of the separatrix for high-frequency, large-amplitude perturbations. This provides a correction to the stochastic layer width, applicable to large amplitude perturbations.
Area of Science:
- Physics
- Applied Mathematics
- Dynamical Systems
Background:
- Perturbations in dynamical systems can lead to complex behaviors, including the formation of stochastic layers.
- Understanding the splitting of the separatrix is crucial for analyzing the stability and chaotic dynamics of such systems.
Purpose of the Study:
- To calculate the exponentially small splitting of the separatrix for a specific type of perturbation.
- To determine the correction to the width of the stochastic layer resulting from this splitting.
Main Methods:
- Analytical calculation of separatrix splitting for high-frequency, large-amplitude perturbations.
- Derivation of the correction term for the stochastic layer width.
Main Results:
- The exponentially small splitting of the separatrix was successfully calculated.
- A quantitative correction to the width of the stochastic layer was obtained.
Conclusions:
- The obtained results provide a precise analytical description of the stochastic layer width under large amplitude perturbations.
- The findings are applicable to systems exhibiting chaotic dynamics driven by high-frequency, large-amplitude perturbations.