Answer
Literature: The Heian period influenced present-day Japan's literature by introducing the use of kana characters, which allowed for the creation of works in the Japanese language.
Music: The Heian period influenced present-day Japan's music by introducing court music, which is still performed today and has become an important part of Japanese cultural heritage.
Poetry: The Heian period influenced present-day Japan's poetry by introducing the tanka form, which is still widely used in modern Japanese poetry.