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Traces and determinants of strongly stochastic operators
1Niels Bohr Institute, Blegdamsvej 17, 2100 København Ø, Denmark. dettmann@nbi.dk
Summary
This study extends periodic orbit theory to stochastic systems by evaluating path integrals. Rapid convergence was demonstrated for the logistic map with additive Gaussian noise, showing its effectiveness for chaotic dynamics.
Area of Science:
- Physics
- Mathematics
- Dynamical Systems
Background:
- Periodic orbit theory analyzes chaotic systems using properties of deterministic evolution operators.
- Stochastic dynamics require different methods, like path integral evaluation, for trace calculations.
Purpose of the Study:
- To adapt periodic orbit theory for stochastic dynamics.
- To demonstrate a numerical method for evaluating path integrals in chaotic systems.
Main Methods:
- Discusses techniques for evaluating path integrals numerically.
- Applies these methods to the logistic map with additive Gaussian noise.
Main Results:
- Shows rapid convergence for the logistic map across various lambda values under strong noise.
- Demonstrates effectiveness for all noise levels at a fixed lambda=5.
Conclusions:
- Path integral evaluation provides an effective method for analyzing stochastic chaotic systems.
- The approach shows promise for calculating long-time properties of noisy dynamical systems.
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