## The dynamics of a magnetic field around a heteroclinic structure |

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angle associated to equilibrium associated to p+ basin of attraction closed orbit common boundary cone Kg configuration of wires ct,y Denote diffeomorphism dimensional heteroclinic dimensional subspace direct sum dynamical system eigenspaces of J+ eigenvalues associated eigenvectors t'i equilibrium cone equilibrium points p+ family of periodic field H field J+ Fix(R gradient field hence heteroclinic circle heteroclinic manifold heteroclinic orbit heteroclinic semicircles heteroclinic structure hyperbolic equilibrium points investigate the dynamics involution magnetic field magnetic-type vector field nonperiodic orbit orthogonal wires parameters periodic orbits phase portrait phase space Proof properties Proposition pseudo-Poincare map respectively rot(H saddle equilibrium points saddle type equilibrium semiline SEMINARUL DE MECANICĂ spatial polycycle stable and unstable stable submanifold stable subspace stable/unstable manifold stable/unstable plane submanifold containing subspace Fix(S symbolic computation symmetric tangent Theorem topological type transversal intersections two-dimensional invariant manifolds type equilibrium point unbounded field line unique field surface University of Timişoara unstable sets Wu(p Wv(p zero