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Robust Wada boundaries and entropy scaling in pp-wave spacetimes
Pedro Henrique Barboza Rossetto1, Vanessa Carvalho Andrade2, Daniel Müller2
1Escola de Artes, Ciências e Humanidades, Universidade de São Paulo Rua Arlindo Bettio, CEP 03828-000, 1000 São Paulo, SP, Brazil.
Chaos (Woodbury, N.Y.)
|June 22, 2026
Summary
The Wada property of escape basins in polynomial potentials remains robust. Dynamical uncertainty increases with polynomial degree, confirming fractal basin boundaries and enhanced unpredictability.
Area of Science:
- Theoretical physics
- Dynamical systems theory
- General relativity
Background:
- Geodesic motion in pp-wave spacetimes is analogous to classical particle dynamics in polynomial potentials.
- Understanding the complexity of dynamical systems is crucial for predicting their behavior.
Purpose of the Study:
- To investigate the dynamics of geodesics in pp-wave spacetimes with polynomial profiles.
- To analyze the robustness of the Wada property and quantify dynamical uncertainty.
- To characterize the fractal nature of basin boundaries.
Main Methods:
- Studying the motion of classical particles in two-dimensional harmonic polynomial potentials.
- Analyzing the Wada property of escape basins under varying polynomial degrees.
- Computing basin entropy (Sb) and boundary basin entropy (Sbb) for quantitative analysis.
Main Results:
- The Wada property of escape basins is robust to changes in polynomial degree.
- Basin entropy (Sb) and boundary basin entropy (Sbb) increase monotonically with polynomial degree.
- Boundary basin entropy (Sbb) exceeds ln(2) for n > 3, confirming fractal basin boundaries.
Conclusions:
- The dynamics of geodesics in pp-wave spacetimes exhibit complex behavior analogous to classical systems.
- Increasing polynomial degree enhances dynamical uncertainty and unpredictability.
- The fractal nature of basin boundaries is confirmed, indicating intricate system dynamics.
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