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Phase transition in the singularity spectrum of an intermingled basin
Hiromi G Ishikawa1, Takehiko Horita1
1Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuencho, Sakai 599-8531, Japan.
Physical Review. E
|January 20, 2018
Summary
This study introduces a solvable model for intermingled basins, revealing a phase transition in their multifractal structure. The findings highlight two distinct orbital phases within asymmetric systems.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Fractal Geometry
Background:
- Intermingled basins are complex structures in dynamical systems.
- Characterizing their multifractal properties is challenging.
- Existing models may not fully capture their intricate scaling behavior.
Purpose of the Study:
- To introduce a solvable two-dimensional piecewise linear mapping model.
- To characterize the multifractal structure of intermingled basins.
- To analyze the singularity spectrum and identify phase transitions.
Main Methods:
- Utilizing multifractal formalism.
- Introducing a partition function for analysis.
- Determining the singularity spectrum to assess local scaling properties.
Main Results:
- The model successfully characterizes multifractal structures.
- Asymmetric systems exhibit a phase transition in the singularity spectrum.
- Two distinct orbital phases (local chaotic and global nonhyperbolic) were identified.
Conclusions:
- The developed model provides insights into intermingled basin dynamics.
- Phase transitions in singularity spectra indicate different dynamical regimes.
- The study elucidates the interplay between chaotic and nonhyperbolic motions.
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