Bessa, MárioRodrigues, Alexandre A. P.2023-05-252023-05-252016M. Bessa, A. Rodrigues, Dynamics of conservative Bykov cycles: Tangencies, generalized Cocoon bifurcations and elliptic solutions, 261, 2, 1176-1202, 20160022-0396http://hdl.handle.net/10400.2/13843This paper presents a mechanism for the coexistence of hyperbolic and non-hyperbolic dynamics arising in a neighbourhood of a conservative Bykov cycle where trajectories turn in opposite directions near the two saddle-foci. We show that within the class of divergence-free vector fields that preserve the cycle, tangencies of the invariant manifolds of two hyperbolic saddle-foci densely occur. The global dynamics is persistently dominated by heteroclinic tangencies and by the existence of infinitely many elliptic points coexisting with non-uniformly hyperbolic suspended horseshoes. A generalized version of the Cocoon bifurcations for conservative systems is obtained.engHeteroclinic bifurcationsTangenciesGeneralized Cocoon bifurcationsChiralityElliptic solutionsjournal article10.1016/j.jde.2016.03.040