Averaging methods for finding periodic orbits via Brouwer degree

By Adriana Buica, Jaume Llibre. 2004

351 citations recorded by the source corpus.

Subfields: Astronomy and Astrophysics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4d97e146c6944a9d0c3b758892707b3900554c97

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In Statistical and Nonlinear Physics

Citations in the corpus

Bifurcation of limit cycles in piecewise smooth systems via Melnikov function (2015, methodology): “One is to use the Melnikov function established in [6], the other averaging method developed in [1, 8, 12].”
Limit cycles of cubic polynomial vector fields via the averaging theory (2007, methodology): “Finally, the last one in based on the averaging theory, see for instance [3, 18, 20].”
On the limit cycles of polynomial vector field (2011, background): “The averaging theory of third order for studying specifically periodic orbits was developed in [4].”
Limit cycles for discontinuous quadratic differential systems with two zones (2014, methodology): “The following result of [4] provides a way for transforming (9) in this standard form.”
Averaging theory at any order for computing periodic orbits (2013, background): “The averaging theory of first order for studying periodic orbits of the differential equations (1) in arbitrary finite dimension is very classical (see for instance [9, 10]), until third order was developed in [1].”
On the birth of limit cycles for non-smooth dynamical systems (2012, methodology): “In [21] Llibre, da Silva and Teixeira studied singular perturbations problems in dimension three which are approximations of discontinuous vector fields proving that the regularization process developed in [24] produces a singular problem for which the discontinuous set is a center manifold, moreove”
Periodic solutions of nonlinear periodic differential systems with a small parameter (2006, methodology): “It is easy to see now that the well known averaging method (see, for example [9, 2]) is obtained as consequence of the above Corollary.”
Higher order averaging theory for finding periodic solutions via Brouwer degree (2014, methodology): “Thus, the main theorem stated in this paper extends the results of Buica and Llibre [5] to an arbitrary order in a small parameter ε.”