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math.DS2011
Unobservable Planar Bimodal Linear Systems: Miniversal Deformations, Controllability and Stabilization
Josep Ferrer, M. Dolors Magret, Juan R. Pacha +1
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focu…
math.DS2011
Transversality of homoclinic orbits to hyberbolic equilibria in a Hamiltonian system, via the Hamilton--Jacobi equation
Amadeu Delshams, Pere Gutiérrez, Juan R. Pacha
We consider a Hamiltonian system with 2 degrees of freedom, with a hyperbolic equilibrium point having a loop or homoclinic orbit (or, alternatively, two hyperbolic equilibrium poi…