Period doubling bifurcations in a two-box model of the Brusselator
Two theorems about period doubling bifurcations are proved. A special case, where one multiplier of the homogeneous solution is equal to +1 is discussed in the Appendix.
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.
Periodic solution of certain second order differential equation
Periodic solutions of a three-species food chain model.
Periodic solutions of the Rayleigh equation with damping of definite sign
The existence of a non-trivial periodic solution for the autonomous Rayleigh equation is proved, assuming conditions which do not imply that has a definite sign for large. A similar result is obtained for the periodically forced equation .
Perturbations of quadratic hamiltonian systems with symmetry
Phase portraits of planar vector fields: Computer proofs.
Polynomial Riccati equations with algebraic solutions
We consider the equations of the form dy/dx = y²-P(x) where P are polynomials. We characterize the possible algebraic solutions and the class of equations having such solutions. We present formulas for first integrals of rational Riccati equations with an algebraic solution. We also present a relation between the problem of algebraic solutions and the theory of random matrices.
Prolungamento dellacurva integrale del sistema di equazioni differenziali sull’insieme singolare. Teoria e applicazioni
Pseudo-abelian integrals on slow-fast Darboux systems
We study pseudo-abelian integrals associated with polynomial deformations of slow-fast Darboux integrable systems. Under some assumptions we prove local boundedness of the number of their zeros.