Is it true that buddhists point out that the primary feature of the universe is stability?

No. According to Buddhism, the primary feature of the universe is change.

Buddhism declares that there are five processes on which no human being has control and which none can ever change.

These five processes are namely, the process of growing old, of not falling sick, of dying, of decay of things that are perishable and of the passing away of that which is liable to pass. Buddhism however suggests that escape from these is possible and it's through Nirvana.

Insight into impermanence is central to Buddhist practice. Buddhist practice points us toward becoming equanimous in the midst of change and wiser in how we respond to what comes and goes.

According to Hinduism, impermanence can be overcome by locating and uniting with the center of permanence that exists within oneself. This center is the Soul or the self that is immortal, permanent and ever stable.

Know more about the Buddhist concept of impermanence at Urbandharma.org and Insightmeditationcenter.org.

https://www.urbandharma.org/udharma8/imperm.html

Monday, May 01 2017
Source: http://homepages.rpi.edu/~verwyc/Zen.htm