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Period function's convexity for Hamiltonian centers with separable variables

100%
Sabatini M.
Annales Polonici Mathematici
|
2005
|
tom 85
|
nr 2
153-163
EN
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.
2
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Commutativity of flows and injectivity of nonsingular mappings

100%
Sabatini M.
Annales Polonici Mathematici
|
2001
|
tom 76
|
nr 1-2
159-168
EN
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.
3
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A Note on the Divergence-Free Jacobian Conjecture in ℝ²

100%
Sabatini M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2009
|
tom 57
|
nr 2
109-115
EN
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.
4
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Quadratic Isochronous centers commute

100%
Sabatini M.
Applicationes Mathematicae
|
1999
|
tom 26
|
nr 3
357-362
EN
We prove that every quadratic plane differential system having an isochronous center commutes with a polynomial differential system.
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