Possibly burning Bush?

That looks like Euonymus alatus, aka Burning Bush. It has become an invasive plant in Connecticut, Virginia, Pennsylvania, and Illinois, so you might reconsider transplanting it. There are plants that do well in hot, dry conditions; your choice will depend on your other requirements. Are you trying to stabilize the hillside?

Here is a link that might be useful: Global Invasive Species Initiative

So although it not invasive on Long Island where I live it is best to toss it in the trash?
Ok, I actually have two planted by previous owners both will be tossed in the trash
Yes I have an eroding hillside that I am trying to create into a garden, along with stabilizing it somewhat. It lacks soil, mostly sand that when you dig in it it erodes more.
I have been putting tons of curbside leaves on the hill as mulch and to help eventually create soil but this takes time.

The leaves help decrease erosion by letting the rain hit the leaves rather then the soil, sort of cushions the fall of the rain.
Any plants that would help with erosion would be great. It is east facing with some shade. Gets moring sun. I enjoy the birds, butterflies and the bees.
Part of the problem with trees and bushes on the hillside is size. If they get so big that they shade the understory and nothing grows at the soil level erosion increases.

I found two Viburnum at the curb, landscaper bushes that must have not been good enough for the home owner. I put those on the hill and they seem to be doing alright. I did that in the fall of 06.
Thanks for the info on the burning bush.. Cherry

Yep, "Burning Bush".

The corky ridges are how we're identifying the plant, FYI, cherry.

If you have only morning sun on the hillside, how is it hot? You might consider native lowbush blueberries, possibly bayberry, and heaths and heathers. They all do well in well-draining conditions.

Although E. alatus may not be on the NY state's list of invasive plants, it should be and probably will be soon. I applaud you for taking the high road and removing it!

More shrubs for erosion control:

Ceanothus
Cistus
Cotoneaster
Hypericum calycinum
Juniperus (ground cover)
Mahonia repens
Rhamnus crocea ilicifolia
Rosa rugosa
Rosmarinus officinalis
Symphoricarpos

Perennials:
Polygonum
Vinca
Ajuga
Hosta
Lavandula

Dax

It is a good idea to plant a variety of plants on a hillside. I don't know how unstable it is, and if you might consider terracing or stabilizing it physically before planting.

Here is a link for a website that might give you some ideas. Here is another from Hume Seeds. Hope they help. http://www.humeseeds.com/hilside.htm

Here is a link that might be useful: how to landscape a hillside