överföringsoperatorer
Överföringsoperatorer, or transfer operators in English, are mathematical objects used in the study of dynamical systems, particularly in chaos theory and ergodic theory. They are linear operators that act on function spaces associated with the system. The core idea is to describe how the probability distribution of a system's state evolves over time. If a system evolves according to a map T, the transfer operator acts on a function describing the density of states and transforms it to a new density function after one time step.
These operators are fundamental because they capture the statistical behavior of the system. For example, the
The definition and properties of transfer operators depend heavily on the specific dynamical system. For discrete-time