The Equivalence Problem in Analytic Dynamics for 1-Resonance

نویسندگان

چکیده

Abstract When are two germs of analytic systems conjugate or orbitally equivalent under an change coordinates in a neighborhood singular point? The present paper, survey nature, presents research program around this question. A way to answer is use normal forms. However, there large classes dynamical for which the form diverges. In we discuss case singularities normalizing transformation k -summable, thus allowing provide moduli spaces. We explain common geometric features these singularities, and show that study their unfoldings allows understanding both themselves, obstructions convergence transformations. also some spaces generic -parameter families unfolding such singularities.

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ژورنال

عنوان ژورنال: Arnold mathematical journal

سال: 2022

ISSN: ['2199-6806', '2199-6792']

DOI: https://doi.org/10.1007/s40598-021-00196-6