This is the 12094th most frequent Russian word.
известному
"Известному" - "to the famous" or "to the well-known" (dative case).
The word 'известному' is in the dative case, modifying the noun 'actor' (актеру), describing their renown or fame.
Я написал письмо известному актеру.
I wrote a letter to the famous actor.
Here, 'известному' is used to describe 'writer' (писателю) and it's in the dative case due to the verb 'посвящать' which is commonly used with the dative case to indicate to whom something is dedicated.
Этот памятник посвящен известному писателю.
This monument is dedicated to the famous writer.
In this sentence, 'известному' qualifies 'inventor' (изобретателю), and is in the dative case as required by the participle 'посвящённый' which often governs the dative case.