The Dynamics of a Magnetic Field Around a Heteroclinic Structure |
Common terms and phrases
A₁ A₂ angle arctan associated to equilibrium associated to p+ basin of attraction bc-a 1+s boundary bc-a(1+s Bs(p c₁ closed orbit common boundary configuration of wires Denote DH(p+ diffeomorphism dimensional heteroclinic dimensional subspace direct sum eigenspaces eigenvalues associated eigenvectors equilibrium cone equilibrium points p+ family of periodic field H Fix(S gradient field hence heteroclinic manifold heteroclinic orbit heteroclinic semicircles heteroclinic structure hyperbolic equilibrium points investigate the dynamics K₁ linear vector field magnetic field magnetic-type vector field parameters periodic orbits phase portrait phase space Proof properties Proposition pseudo-Poincaré map rot(H saddle type equilibrium semiline SEMINARUL DE MECANICĂ spatial polycycles stable and unstable stable submanifold stable subspace stable/unstable plane subspace Fix(R Sx(p+ symmetric t₁ tangent space Theorem Timişoara Department topological type transversal intersections two-dimensional invariant manifolds type equilibrium point unbounded field line unique field surface University of Timişoara unstable sets W(p+ zero