KAM THEORY. Part 3. Applications
Mauricio Garay, Duco van Straten
TL;DR
This paper applies advanced normal form theorems in Kolmogorov spaces to classical problems in singularity deformations, vector field normalization, and Hamiltonian invariant tori, providing new insights into these areas.
Contribution
It introduces novel applications of Kolmogorov space normal form theorems to classical dynamical systems and singularity theory.
Findings
Deformations of hypersurface singularities analyzed using normal forms
Normal forms of vector fields derived in specific contexts
Existence and stability of invariant tori in Hamiltonian systems demonstrated
Abstract
We apply the general normal form theorems in Kolmogorov spaces to three classical cases: deformations of hypersurface singularities, normal forms of vector fields and invariant tori in Hamiltonian systems.
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Taxonomy
TopicsGeometric and Algebraic Topology · Quantum chaos and dynamical systems · Mathematical Dynamics and Fractals