Effects of memory-induced effective dimensionality on dynamical invariants and attractor geometry

Investigate how memory-induced effective dimensionality influences Lyapunov spectra, entropy production rates, and the geometry of attractors in non-Markovian chaotic systems.

Background

The paper identifies a memory-controlled transition in universality classes and derives a fractional scaling law for the largest Lyapunov exponent in a one-dimensional non-Markovian logistic map. Beyond the largest exponent, the full Lyapunov spectrum, entropy production, and attractor geometry are natural diagnostics of high-dimensional chaotic behavior.

Understanding how temporal correlations modify these invariants would extend the minimal model’s insights to richer systems where multiple expansion/contraction directions and complex attractor structures are present.