分野別セミナー

In this talk, we first review the notion of hyperbolicity introduced by Smale and some paradigmatic examples of hyperbolic dynamics (horseshoes and Anosov systems).
Next we discuss the necessity of introducing new forms of "weak hyperbolicity" and present some examples. The weakest form of hyperbolicity is "domination" (existence of a dominated splitting). Finally, we discuss the generation of non-dominated dynamics and some features associated to these dynamics. This leads to the so-called "wild dynamics", whose emblematic example is Newhouse coexistence phenomenon of infinitely many sinks associated to homoclinic tangencies.