Pavao Mardesi'c

activity

20122025

most citedUnfoldings of saddle-nodes and their Dulac time

2 citations · 2 across the 4 of their papers we have counts for

collaborators

4 papers

math.CA2025

Noetherianity and length of Melnikov functions

Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1

We study foliations in $C^{2}$ given by polynomial deformations of the form $d H + ε η = 0$ , with $γ (t) \subset H^{- 1} (t)$ a family of cycles. The \emph{Poincaré first return map}…

math.CA2024

Nilpotence of Orbits under Monodromy and the Length of Melnikov Functions

Pavao Mardešić, Dmitry Novikov, Laura Ortiz-Bobadilla +1

Let $F \in C [x, y]$ be a polynomial, $γ (z) \in π_{1} (F^{- 1} (z))$ a non-trivial cycle in a generic fiber of $F$ and let $ω$ be a polynomial $1$ -form, thus defining a polynomial d…

math.DS2015★ 2 cited

Unfoldings of saddle-nodes and their Dulac time

Pavao Mardesić, David Marín, Mariana Saavedra +1

In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we prove uniform regul…

math.DS2012

Inductive Solution of the Tangential Center Problem on Zero-Cycles

Amelia Álvarez Sánchez, José Luis Bravo Trinidad, Pavao Mardesić

Given a polynomial $f\in\C[z]$ of degree $m$ , let $z_{1} (t), ..., z_{m} (t)$ denote all algebraic functions defined by $f (z_{k} (t)) = t$ . Given integers $n_{1} ..., n_{m}$ such that $n_{1} + ... + n_{m} = 0$ …