COMACO · Continuous mappings on compact metrizable spaces

Lines connect the coordinator with its partners. CORDIS does not always give exact coordinates for projects before 2014. These points are placed at city or country level.

Project objective

I propose to study properties of sequences of iterations of a given continuous mapping on a compact metrizable space.From a topological version of the Rosenthal dichotomy, the pointwise closure of the sequence either consists of the pointwise limits of subsequences and then it is called a Rosenthal compact space, or there exists a chaotic" subsequence, where chaos is manifested by the fact the pointwise closure of the subsequence is homeomorphic to a copy of the Cech-Stone compactification of the natural numbers.I propose to study the following two basic problems and their generalizations:- for a given continuous mapping f, identify in terms of dynamical properties of f, when the closure of iterations of f is a Rosenthal compact space.- construct a continuous mapping f, such that the closure of iterations of f is a complicated Rosenthal compact space in terms of ordinal ranks on the class of Rosenthal compact spaces."

Original text from CORDIS.

Participants

• INSTITUT DE MATHéMATIQUES DE JUSSIEUCoordinatorCity levelFrance

Links

• View on CORDIS