Are there exercises to do that will not increase heart rate?

I am a 48 yo female that recently had a light stroke (my left side has no pain or temperature sensation, but I can use it). The reason for the stroke is unknown. I am overweight, but have no heart disease and do not smoke. I had just gotten into exercising before I had the stroke. During my MRI it was was found the stroke affected my medulla and cerebellum. It was also found that I have an aneurysm in the vertebral artery. My doctors have put me on plavix, and I am restricted to having no caffeine, no chocolate, and cannot raise my heart rate because of the aneurysm. Are there any exercises you know I can do that will not raise my heart rate?