Examples of horseshoe

• Unfolding homoclinic tangencies inside horseshoes: hyperbolicity, fractal dimensions and persistence of tangencies.

• Cascades of period doubling bifurcations: a prerequisite for horseshoes.

• Unfolding homoclinic tangencies inside horseshoes: hyperbolicity, fractal dimensions and persistent tangencies.

• There are horseshoes in these examples on which the geodesic flow has strongly stochastic behavior.

• A second aspect is whether the unstable manifold intersects the strong stable manifold of the saddle-node (as in the case of the saddle-node horseshoes).

• As the section implies, there were complete horseshoes in tiers 1, 2 and 3; the fourth and fifth were interrupted by the galleries at the north end of the auditorium.

• Are there (uniformly hyperbolic) horseshoes?

• Global strange attractors after collision of horseshoes with periodic sinks.