Bifurcation of periodic solutions from inversion of stability of periodic O.D.E.'S.
Quadratic Isochronous centers commute
We prove that every quadratic plane differential system having an isochronous center commutes with a polynomial differential system.
Commutativity of flows and injectivity of nonsingular mappings
A relationship between jacobian maps and the commutativity properties of suitable couples of hamiltonian vector fields is studied. A theorem by Meisters and Olech is extended to the nonpolynomial case. A property implying the Jacobian Conjecture in ℝ² is described.
Period function's convexity for Hamiltonian centers with separable variables
A convexity theorem for the period function T of Hamiltonian systems with separable variables is proved. We are interested in systems with non-monotone T. This result is applied to proving the uniqueness of critical orbits for second order ODE's.
A Note on the Divergence-Free Jacobian Conjecture in ℝ²
We give a shorter proof to a recent result by Neuberger [Rocky Mountain J. Math. 36 (2006)], in the real case. Our result is essentially an application of the global asymptotic stability Jacobian Conjecture. We also extend some of the results of Neuberger's paper.
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