Topological dynamics for groups definable in real closed field

The Ellis Group Conjecture and Variants of Definable Amenability

“…If G{ApGq is definably isomorphic to a group definable over the reals, this result can be improved. We have the following result by Yao [16]:…”

“…In [9], a wide range of counterexamples have been produced by calculating the Ellis groups for the flows of groups definable in o-minimal expansions of the reals admitting definable compact-torsion-free decomposition. These results have been generalized in [16] to allow the calculation of the Ellis groups over larger models, establishing the isomorphism with groups calculated over the reals. A tangent case of definably amenable groups definable in o-minimal expansions of arbitrary real closed fields have been solved in [14].…”

Definable topological dynamics for trigonalizable algebraic groups over Qp

“…In the recent years there has been growing interest in the interaction between topological dynamics and model theory. This approach was introduced by Newelski [10], then developed by a number papers, include [15], [6], [3], [20] and [17], and now called definable topological dynamics. Definable topological dynamics studies the action of a group G definable in a structure M on its type space S G (M) and tries to link the invariants suggested by topological dynamics (e.g enveloping semigroups, minimal subflows, Ellis groups...) with model-theoretic invariants.…”

Definable Topological Dynamics

“…Topological dynamics was introduced to model theory by Newelski in [20,21] and then further developed by various authors, e.g. in [8], [10], [29], [2], [14] and [15]. There are several natural categories to develop topological dynamics in model theory.…”

“…Newelski in [20,21] and then further developed by various authors, e.g., in [2,8,10,14,15,29]. There are several natural categories to develop topological dynamics in model theory.…”