Does DumbleDore Have a HorCrux ?

Interesting, i will start with few examples...from HP books.

-> DD's knowledge about Horcrux, (from HBP).

"A bit... or more," said Dumbledore. "You heard Voldemort, what he particularly
wanted from Horace was an opinion on what would happen to the wizard who created
more than one Horcrux, what would happen to the wizard so determined to evade death
that he would be prepared to murder many times, rip his soul repeatedly, so as to store it
in many, separately concealed Horcruxc. No book would have given him that
information. As far as I know — as far, I am sure, as Voldemort knew — no wizard had
ever done more than tear his soul in two."

So, DD knows a wizard who created a HorCrux, and also Voldie knows about him.

-> DD's prediction about Nagini as Voldemort's Horcrux, The reason which DD gives is

".......I think he is perhaps as fond of her as he can be of anything; he certainly likes
to keep her close, and he seems to have an unusual amount of control over her, even for
a Parselmouth."

If voldemort has unusual control over nagini and if it is a Horcrux for him, what about the unusual control DumbleDore has on Fawkes,

Few examples for DD's control over Fawkes

1. (from Chamber of Secrets after Tom dies).
............“First of all, Harry, I want to thank you,” said Dumbledore, eyes twinkling again. “You must have shown me real loyalty down in the Chamber. Nothing but that could have called Fawkes to you.” He stroked the phoenix, which had fluttered down onto his knee. Harry grinned awkwardly as Dumbledore watched him..........."

2. (from GOF when Priori Incatetem comes Up).

"..........It was the sound of hope to Harry... the most beautiful and welcome thing he had ever heard in his life... He felt as though the song were inside him instead of just around him... It was the sound he connected with Dumbledore, and it was almost as though a friend were speaking in his ear...Don't break the connection.I know. Harry told the music, I know I mustn't... but no sooner had he thought it,..."

Whom do you think said the above words in Harry's ear ?

3. (from OOTP when Tom duels with DD)

"........Fawkes swooped down in front of Dumbledore, opened his beak wide and swallowed the jet of green light whole: he burst into flame and fell to the floor, ......."

So, I strongly feel that Fawkes is a Horcrux for DD.

One incident from the 6th book also points to DumbleDore's Horcrux,
During one of his private classes with Harry, Dumbledore examines memories of different people including his own. There Dumbledore instead of extracting memory from his head, pours his own memory from a bottle and shows the contents to harry.

Why did he do like that ?

What answers this question is, it's not the real Dumbledore who has taken harry's classes, but it's the copy of DD (from Horcrux).

It's the Copy of DumbleDore who went to the cave with harry and who pretended to be dead on the top of castle.