Question

Do the same avatars repeat in each chaturyuga?

Answer

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This might give you an idea of how yugas are divided. As far as same thing getting repeated every chaturyug ,i do not reckon any mention of that but in Devadutta Patanaik book "SITA"

Yum comes Ayodhya to take Lord Ram life but he couldn't enter as Hanuman is guarding the gates of Ayodhya. Lord Ram knew about this, so to distracts Hanuman from guarding the gate he drops his ring in river and ask Hanuman to fetch it. Hanuman dive inside the river but he donot find the ring but meet nagas of nagalok. He enquires about the ring but they refuse to tell him until he tell them the story of Lord Ram. So he tells the whole story to them and then enquires about ring. They point in the direction where he can find the ring . When he reaches the location he see heap of rings, each exactly similar to other. He ask which one is of Lord Ram. They say "As many ring, so mang Ram". Life is a cycle. What has happened in the past will again happen in future.Each time a monkey comes to fetch the ring,a Ram dies up there. Hanuman rushes back to Adyodhya to see Ram took Jal samadhi. Block quote

Devdutta researches very deeply before writing his book. So he must taken this from somewhere.

Apart from that We indian believe that what has happened in past will again happen in future, that is why we have a word "kal" for both yesterday and tomorrow.

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