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The aim is to develop a geometric framework for dissipative dynamical systems with unique characteristics, emphasizing limit cycles and stability.

May 25, 2026Open Access

Generative Contact Mechanics: A Geometric Framework for Dissipative Systems with Structured Limit Cycles

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The aim is to develop a geometric framework for dissipative dynamical systems with unique characteristics, emphasizing limit cycles and stability.
Introduced the dm3 system as a smooth Riemannian manifold with a hyperbolic limit cycle and a Lyapunov function.
Constructed a complete operator algebra to describe system properties like expansion and unification.
Formalized the framework based on eight axioms governing the system's behavior.
The dm3 system demonstrates a unique exponentially stable hyperbolic limit cycle with stochastic stability below a threshold τ.
The category of dm3 systems is closed under a unification operator, indicating that unification reduces noise tolerance.
The operator algebra exhibits C¹-structural stability with a calculated stability radius ε₀.

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This theoretical framework establishes dissipative dynamics in systems with structured limit cycles, suggesting new stability insights.

Pablo Nogueira Grossi (2026) studied this question.

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