Stability versus chaos for a partial differential equation
The main purposes of the presented paper is to investigate a semiflow generated by a first-order partial differential equation, to show that stability and chaos depend on the proper choice of the phase space and to develop a method in order to construct an invariant measure under the semiflow \(\{S_t\}_{t\geq 0}\). The paper is organized as follows. The introduction contains several assumptions and preliminary remarks and is followed by Section 2, ``Main results''. Section 3, ``Invariant measure'' developes the construction of an invariant measure under the shift semiflow \(\{S_t\}\). Clear and accurate, this study opens new ways for studying the stability of chaotic systems.
scientific article; zbMATH DE number 1783809