Stability, Chaos, and Structural Comparison in the Energetic–Elastic N-Body Model

Abstract

The Energetic–Elastic N-Body Model (EETBM) is a Hamiltonian framework in which Newtonian pair potentials are replaced by quadratic elastic interactions. We establish collision-free well-posedness, energy-barrier and comparison bounds, stability criteria, and conditional KAM persistence. A central result proves that, for arbitrary N, every fixed collision-free collinear ordering sector with a connected positive spring graph is an exactly linear, spectrally stable oscillator system, excluding nontrivial collinear homoclinic dynamics. We also derive a cohomological obstruction to the standard Moser path between EETBM and Newtonian dynamics, dimensionless finite-time comparison bounds, and conditional persistence results. The analysis identifies the model’s nonlinearity as fundamentally geometric and clearly separates proved, conditional, and open results.

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