Cyclical time in Buddhism

I've been learning about time and the varyous perspectives that it is viewed through, and it seems like there are two main ways of thought. The first, generally associated as a western mindset, is that time is linear. The second, and this is generally considered more eastern, is that time is considered cyclical. I'm pretty sure that this is also a common way-of-thought in Hunduism, but I'm, in particular, wanting to learn more about the nature of time from a buddhist perspective. Of what I have read sutra-wise (pretty much just the Lotus Sutra), I have only seen time's cyclality being alluded to once, when Shakyamuni Buddha is saying that, at the end of a kalpa, when the world is consumed by fire, his pure land will, although appearing to burn with the rest of the world, stay safe and untouched. I assume from this that at the end of kalpas, it was considered that the world would burn (maybe signifying the start of a new cycle). Anyhow, I'm just wanting to know more about the nuances of Buddhist-cyclical time and how one can comprehend/view the world in such a way.