The term “canard cycle” was coined by Benoit and al in [BCDD81] in the context of the theory
of singular perturbations in two-dimensional differential equations. Roughly speaking, a …

In the present paper we focus on the problem of the existence of strange pseudohyperbolic
attractors for three-dimensional diffeomorphisms. Such attractors are genuine strange …

In this paper we introduce the notion of fractal codimension of a nilpotent contact point p, for
λ= λ 0, in smooth planar slow–fast systems X ϵ, λ when the contact order n λ 0 (p) of p is …

The goal of our paper is to study canard relaxation oscillations of predator–prey systems
with Holling type II of functional response when the death rate of predator is very small and …

This paper deals with local bifurcations occurring near singular points of planar slow-fast
systems. In particular, it is concerned with the study of the slow-fast variant of the unfolding of …

In our paper we present a fractal analysis of canard cycles and slow-fast Hopf points in 2-
dimensional singular perturbation problems under very general conditions. Our focus is on …

In this article, we introduce the use of Lambert function to develop further the global
perturbation theory of an integrable Liénard equation which displays a symmetric center. We …

In this paper, we study the Chebyshev property of the 3-dimentional vector space $
E=\langle I_0, I_1, I_2\rangle $, where $ I_k (h)=\int_ {H= h} x^ ky\, dx $ and $ H (x, y)=\frac …

Dumortier and Roussarie proposed a conjecture in their paper (2009, Discrete Con. Dyn.
Sys., 2,723-781): For any $ q\in {\mathbb {N}} $, the Abelian integrals $ J_ {2j+ 1}(h)=\int …

Dumortier and Roussarie formulated in (Discrete Contin Dyn Syst 2: 723–781, 2009) a
conjecture concerning the Chebyshev property of a collection I_0, I_1, ..., I_n I 0, I 1,…, I n of …