The CAPD library has been used in several articles in which chaotic dynamics, bifurcations, heteroclinic/homoclinic solutions and periodic orbits were studied.
 The existence of simple choreographies for the nbody problem
 Homoclinic and heteroclinic solutions
 Chaotic dynamics for various ODE's
 Invariant curves through the KAM theory
 Cocoon bifurcations
 Rigorous verification of period doubling bifurcations for ODE's
 Rigorous numerics for homoclinic tangencies
 Uniformly hyperbolic attractors for Poincare maps
 Rigorous numerics for dissipative PDE's
 Normally Hyperbolic Invariant Manifolds
 Dynamics of the universal areapreserving map associated with period doubling (written by Tomas Johnson)
Cocoon bifurcations
Cocoon bifurcation is a global phenomenon which occurs in 3D reversible ODE's. It has been shown [1] that under some nondegeneracy condition such a vector fields possesses a cascade of heteroclinic tangencies accumulating to new born saddlenode periodic solution. Because of the shape of unstable and stable manifolds of the equilibria these cascades are called cocooning bifurcations. In [2] we have proved that such a cascade of cocoon bifurcations occurs in the Michelson system x''' + x' + 0.5x^{2} = c^{2} where the periodic orbit to which tangencies accumulate is for some parameter value from the interval [1.2662323370670545, 1.2662323370713253]. The proof required rigorous enclosure for the first and second order derivatives of the Poincare map. Here we used C^{1}C^{2}solvers from the CAPD to obtain rigorous bounds for these derivatives. References:

The proof required rigorous estimation of the unstable set of the nonhyperbolic periodic orbit in an explicit neighbourhood of this orbit. 