TY - JOUR
AU - I. V. Atamas'
AU - V. I. Slyn'ko
PY - 2017/08/25
Y2 - 2020/12/05
TI - Stability of fixed points for a class of quasilinear cascades in the
space conv $R^n$
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 69
IS - 8
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1766
AB - The discrete dynamical systems (cascades) in semilinear metric space of nonempty convex compacts of finite-dimensionalspace are studied. Using the methods of convex geometry of H. Minkowski and A. D. Alexandrov the sufficient conditionsof the stability of the fixed points were established. Under certain restrictions on the mappings generating the cascade, theproblem of asymptotic stability of fixed point of the cascade was reduced to localization of the roots of a polynomial insidethe unit circle in the complex plane. Examples of cascades in the plane were given.
ER -