J
Jaume Llibre
Researcher at Autonomous University of Barcelona
Publications - 1153
Citations - 16371
Jaume Llibre is an academic researcher from Autonomous University of Barcelona. The author has contributed to research in topics: Polynomial & Limit (mathematics). The author has an hindex of 51, co-authored 1082 publications receiving 14337 citations. Previous affiliations of Jaume Llibre include Northwestern University & Polytechnic University of Catalonia.
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Book
Qualitative Theory of Planar Differential Systems
TL;DR: In this article, the authors deal with systems of polynomial autonomous ordinary differential equations in two real variables, and the focus is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability.
Book
Combinatorial Dynamics and Entropy in Dimension One
TL;DR: In this paper, the authors define lifted cycles, lifted cycles cycles and lifted cycles periods for maps of degree different from -1, 0 and 1 periods for map of degree 0, 1 rotation numbers and twist lifted cycles estimate of a rotation interval period for maps with the prescribed set of periods other results.
Journal ArticleDOI
Averaging methods for finding periodic orbits via Brouwer degree
Adriana Buică,Jaume Llibre +1 more
TL;DR: In this article, the problem of finding T -periodic solutions for a differential system whose vector field depend on a small parameter e.g., the displacement function is considered and an answer to this problem can be given using the averaging method.
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Multiplicity of invariant algebraic curves in polynomial vector fields
TL;DR: Several natural definitions of multiplicity for invariant algebraic curves in polynomial vector fields are given and it is shown that there is a natural equivalence between the algebraic viewpoint and the geometric viewpoint.
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On the nonexistence, existence and uniqueness of limit cycles
TL;DR: In this paper, two new criteria for studying the nonexistence, existence and uniqueness of limit cycles of planar vector fields are presented, and a method to derive the shape of the bifurcated limit cycles from a centre is presented.