Bohl exponents and Baire classes of functions
For a linear system of first-order ordinary differential equations, it is well-known that the (in)stability can be described using the characteristic exponents and the Lyapunov exponents. In order to study more subtle stability like the conditional stability, the Russian school has developed further notions of exponents like the Bohl, the conditional Bohl, and the relative Bohl exponents. One of the main contributions of the present paper is to give the corresponding notions for diffeomorphisms by considering their linearization systems. Besides the establishment of the relations between these exponents, the author also obtains some deep results on these exponents, considered as functions of parameters in systems, which are described in terminology of the Baire classes of different orders.
scientific article; zbMATH DE number 6529636
scientific article