This might be something way too trivial but I'm not seeing it yet so if you could explain to me the following I'd be thankful.
On this page http://mathworld.wolfram.com/HomoclinicTangle.html the property "area preservation" is used, but I don't see where this comes from.
Thanks in advance
"Area preservation" is a common hypothesis for dynamical systems. In the setting of that article, it probably means that $\text{Area}(T(A)) = \text{Area}(A)$ for each Borel measurable subset $A$.
However, area preservation is by no means a necessary hypothesis for studying homoclinic connections of surface diffeomorphisms, so I don't see why it is included in that article.