LOCAL PATH-PRESERVING AUTOMORPHISMS IN THE ALGEBRA OF ASYMPTOTICALLY DIFFERENTIABLE FUNCTIONS
Keywords:
Asymptotic differential algebra, local automorphism, differential operator, idempotent, track maintenance.Abstract
This article investigates the structure of asymptotic differential algebras. The main attention is paid to the differential operator of local automorphisms preserving tracks and the property of commutativity. The study showed that if global automorphisms are commutative with the differential operator, then local automorphisms also retain this property. The problem of preserving the differential of complex functions is also considered.
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