2026/02/19 by Vasil Tsanov · 1 voice
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · doi:10.5281/zenodo.18698140
openalex publication_date 2026/02/19 · openalex created_date 2026/02/21 · openalex updated_date 2026/07/01
We develop a scale–independent framework for the classification of astrophysical dynamical systems based on intrinsic spectral–dynamical invariants reconstructed from observational time series.To each system P we associate a spectral invariant σ(P) =(r, ω,λmax,htop,D2,μ,G), encoding frequency rank, Lyapunov spectrum, topological entropy, fractal dimension, invariant measure, and symmetry group of the reconstructed attractor. The invariant σ induces a partition of the space of admissible systems into spectral phases. We prove separating properties for hyperbolic limit cycles and quasi–periodic tori, establish conditional stability of σ under small observational noise, and characterize expansive phases via positive Lyapunov exponent or entropy. A structural trichotomy emerges: linear time evolution on compact attractors either factors through toroidal geometry (cyclic phases), or exhibits intrinsic exponential divergence (expansive phases). The hypersurface λmax=0 acts as a phase boundary between these regimes. This yields a precise mathematical formulation of a linear–cyclic closure principle: although time itself is linear and unbounded, its dynamical realization may close into compact cyclic geometry in non–expansive regimes, while remaining open to chaotic evolution in expansive regimes. Because σ is dimensionless and scale–free, it enables structural comparison of dynamical systems across cosmological distances, suggesting a universal spectral phase structure of astrophysical emitters.