The present work is designed to explore the evolutionary and pulsational properties of low-mass white dwarfs with carbon/oxygen cores .
In particular , we follow the evolution of a 0.33- M _ { \odot } white dwarf remnant in a self-consistent way with the predictions of nuclear burning , element diffusion and the history of the white dwarf progenitor .
Attention is focused on the occurrence of hydrogen shell flashes induced by diffusion processes during cooling phases .
The evolutionary stages prior to the white dwarf formation are also fully accounted for by computing the conservative binary evolution of an initially 2.5- M _ { \odot } Pop .
I star with a 1.25 M _ { \odot } companion , and period P _ { i } = 3 days .
Evolution is followed down to the domain of the ZZ Ceti stars on the white dwarf cooling branch .

We find that chemical diffusion induces the occurrence of an additional hydrogen thermonuclear flash which leads to stellar models with thin hydrogen envelopes .
As a result , a fast cooling is encountered at advanced stages of evolution .
In addition , we explore the adiabatic pulsational properties of the resulting white dwarf models .
As compared with their helium-core counterparts , low-mass oxygen-core white dwarfs are characterized by a pulsational spectrum much more featured , an aspect which could eventually be used for distinguishing both types of stars if low-mass white dwarfs were in fact found to pulsate as ZZ Ceti – type variables .
Finally , we perform a non-adiabatic pulsational analysis on the resulting carbon/oxygen low-mass white dwarf models .