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Generalized Poincaré–Hopf Theorem for Oscillatory Systems under the NMSI–π– γ_diss–e

Author:

Lazarev, Sergiu Vasili

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

September 30, 2025

File:

/Research Papers-Mathematics and Applied Mathematics/Download/10321

Downloads:

Keywords:

Poincaré–Hopf theorem, Dynamic zero, Oscillatory systems, Navier–Stokes regularity, NMSI–π*– γ_diss–e* framework, Topological invariants, Turbulence stabilization

Abstract:

This paper develops a generalized formulation of the Poincaré–Hopf theorem in the context of oscillatory systems described under the NMSI–π*–γ_diss–e* framework. By introducing the concept of dynamic zeros points where vector fields vanish transiently due to oscillatory forcing and dissipative stabilization we extend the classical theorem beyond static topological invariants. The proof combines analytical methods with numerical simulations of augmented Navier–Stokes dynamics, demonstrating that oscillatory systems admit bounded solutions where singularities are replaced by structured dynamic zeros. This generalization offers new perspectives on turbulence, fluid regularization, and nonlinear dynamical systems.

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