Introduction. Theorem for local changes of contractive bounded functions over a compact set. Metrics and norms on the space of finite signed measures, mass transportation problem and maximum principles for basic metrics: Kantorivich-Wasserstein, Fortet–Mourier and total variation.
The maximum principle and the invariance principle in the stability theory of dynamical systems on measures:
a) dynamical systems generated by different types of the Boltzmann-type equations – modeling of particle collisions in a rarefied gas,
b) limit theorems and perturbed dynamical systems with discrete-time – biological models,
c) dynamical systems generated by impulsive Poisson’s equation (known as a stochastic equation with Poisson-type disturbances) – in the modeling of the cell cycle,
d) generalized iterated function systems – mathematical constructions of cell cycle models.
- Nauczyciel: Gacki Henryk