A REMARK ON THE GROBMAN-HARTMAN LINEARIZATION THEOREM FOR VECTOR FIELDS

• Autor(a) principal: Chachapoyas Siesquén, Nancy Carolina
• Data de Publicação: 2022
• Outros Autores: Bravo Vidarte, José Humberto
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Revista Sergipana de Matemática e Educação Matemática
• Texto Completo: https://seer.ufs.br/index.php/ReviSe/article/view/15048

In mathematics, the term ``nonlinear" generally corresponds to a more difficult analysis. Since linear systems are easier to analyze, a key way to understand nonlinear systems is to find out where and when they can be well-approximated by linear systems. In this respect, we have a famous theorem in nonlinear differential equations due to Grobman [Gro59] and Hartman [Har60a], which guarantees us that a vector field of class C1, X : W ⊂ Rn → Rn (where W is an open set and p is a hyperbolic singularity) is topologically conjugated to a linear field A = DX(p) (in a neighborhood of p and 0, respectively).This work aims to prove thatthe conjugation (``change of variables'') in the Grobman-Hartman theorem is always H\"{o}lder continuous. Finally, we will give an example to illustrate our result. Keywords: Vector fields, conjugation, linearization, hyperbolic singularities.