Presentation on theme: "2. Piecewise-smooth maps Chris Budd. Maps Key idea … The functions or one of their nth derivatives, differ when Discontinuity set Interesting discontinuity."— Presentation transcript:
Key idea … The functions or one of their nth derivatives, differ when Discontinuity set Interesting discontinuity induced bifurcations occur when limit sets of the map intersect the discontinuity set
Origin of Square-root-Linear, continuous maps Local behaviour of the Poincare maps of hybrid systems close to grazing impacts [Budd, Nordmark, Whiston] Quasi-local behaviour of the Poincare maps of piecewise-smooth flows close to grazing (The very local behaviour of such flows leads to maps with a piecewise linear map coupled to a map with a 3/2 power law)
All maps have fixed points over certain ranges of Border collision bifurcations occur when for certain parameter values the fixed points intersect with the discontinuity set Get exotic dynamics close to these parameter values
I: Dynamics of the piecewise-linear-continuous map [Feigin, Hogan. Homer, di Bernardo] Fixed points Not all fixed points are admissible!