Generalized curve foliations are a type of foliations that have a similar reduction as the one given by curves. Camacho, Lins Neto, and Sad showed that generalized curve no-dicritical foliations have the same reduction of singularities than their separatrices. In this paper we give a novel proof of Dulac's theorem ([9]) using techniques of Rouille ([19]). This theorem shows that for generalized curve no-dicritical foliations their Newton polygons and their separatrices are equal. Using Dulac's theorem we return to a result (wrongly) stated by Loray, which is notquite right, as noticed by Fernandez, Mozo and, Neciosup. / Foliaciones de tipo curva generalizada son una clase de foliaciones que tienen una reducción de singularidades similar a la que existe para curvas. Camacho, Lins Neto and Sad mostraron que aquellas que son no dicríticas tienen la misma reducción que la de su conjunto de separatrices. En este artículo presentamos una prueba novedosa del teorenma de Dulac utilizando técnicas de Rouillé. Este teorema muestra que para foliaciones no dicríticas de tipo curva generalizada su polígono de Newton y el su conjunto de sepatrices coinciden. Mediante el teorema de Dulac retornamos a un resultado conjeturado por Loray que no es del todo cierto, como fue anotado por Fernández, Mozo y Neciosup.

<p>Predmet istraživanja doktorske disertacije je faktorizacija polinoma dve promenljive sa celobrojnim koeficijentima pomoću njima pridruženih Newton-ovih poligona. Formalizacija potrebnog i dovoljnog uslova za postojanje netrivijalne faktorizacije polinoma dve promenljive sa celobrojnim koeficijentima omogućava konstrukciju efektivnog algoritma za faktorizaciju. Konačno, dobijeni teorijski rezultati su primenjeni na dekodiranje jedne klase Reed &ndash; Solomon kodova, miksa dve kodne reči.</p> / <p>The research subject of the thesis is factorization of bivariate polynomials with integer coefficients via associated Newton polygons. Formalization of the necessary and sufficient condition for the existence of a non &ndash; trivial factorization of an arbitrary bivariate polynomial with integer coefficients obtains theoretical basis for construction of an effective factorization algorithm. Finally, these theoretical results are applied in decoding special class of Reed &ndash; Solomon codewords, mixture of two codewords.</p>

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