TL;DR
This paper introduces operadic dynamics based on Gerstenhaber theory, defining operadic observables, evolution equations, and Lax pairs, with an example of a harmonic oscillator to illustrate the concepts.
Contribution
It presents a novel framework for operadic dynamics, including the formulation of evolution equations and Lax pairs within the Gerstenhaber algebra setting.
Findings
Operadic observables satisfy Gerstenhaber algebra identities.
Operadic evolution equations govern the dynamics of observables.
An example of an operadic harmonic oscillator is constructed.
Abstract
Based on the Gerstenhaber Theory, clarification is made of how operadic dynamics may be introduced. Operadic observables satisfy the Gerstenhaber algebra identities and their time evolution is governed by operadic evolution equation. The notion of an operadic Lax pair is also introduced. As an example, an operadic (representation of) harmonic oscillator is proposed.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation