This book takes the Trojan framework—the union of geometric protection (the Trojan Universality Class) and operational transport diagnostics (thin versus thick chaos)—and applies it to six persistent open problems in nonlinear dynamics. Arnold diffusion, FPUT recurrence, many-body localization, coherent structures in turbulence, universality in dissipative systems, and early warning signals for regime shifts all turn out to share the same underlying architecture.
The central claim is simple: long-lived coherence is not an accident. It happens when a system's instability remains confined—when chaos stays thin. The Trojan framework identifies the protective structure: a two-mode normal form with a spectral gap that suppresses transport. It also identifies exactly how that protection fails: through one of four structural exit mechanisms—separatrix splitting, resonance overlap, spectral gap collapse, or activation of additional modes. Each mechanism produces detectable precursors before failure occurs.
The book proves new theorems for each problem, showing that persistence is architecture, not mystery. A system survives not because nothing irregular happens, but because irregularity is prevented from reaching what matters.
Publication Date: 2026-06-23