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Murray opens Monday in Arthur Ashe Stadium against Alex Bogomolov Jr., of Russia.

Federer, back at the top of the rankings after 25 1/2 months during which Nadal and Djokovic took the spot from him, has a night match Monday against American Donald Young, who is 3-21 this season.

Federer says there’s a difference between how he feels now and last year, when he had two match points in the semifinals against Djokovic, but lost both and closed out his first full season since 2002 without a Grand Slam title.

“I think I felt good last year, but probably felt that maybe, at times, the matches were not always on my racket,” he said. “Whereas maybe this time around, I feel like if I’m playing well, I can dictate who’s going to win or lose.”

Though the women’s game has been more in flux than the men’s of late _ seven different winners over the past seven Grand Slams _ the math turned out essentially the same in 2012: Three of the top four women _ No. 1 Victoria Azarenka (Australia), No. 3 Maria Sharapova (France) and No. 4 Williams (Wimbledon) _ have major titles this year and all need this one to break the tie.

Where things differ is in the way Williams has been playing of late. She lost a total of 17 games over six matches in the Olympics, punctuating it with a 6-0, 6-1 victory over Sharapova in the final _ the kind of drubbing that would have to come to mind if the two should meet in the U.S. Open final on Sept. 8.

Sharapova had two hard-court tuneup tournaments on her schedule, but pulled out of both with a stomach virus.

“I think it was a sign my body just needed to slow down,” she said. “It was a lot of travel, a lot of playing. I had a hectic summer. So, I decided to shut it down until here, because we still have a lot to play towards the end of the year.”

Kim Clijsters, on the other hand, doesn’t have to save any energy for down the road. Win or lose, she says the U.S. Open will be it for her.

“Here,” she said, while pointing to her heart. “You feel when it’s right.”

Clijsters, who missed last year with a stomach-muscle injury, has won her past 21 matches at Flushing Meadows. In 2005, she won the tournament. She didn’t return again until 2009, after she had gotten married and had a daughter, Jada. With virtually no tournament play under her belt in 2009, Clijsters won seven matches to become the first unseeded woman to capture the U.S. Open. It was her first of back-to-back titles.

Because of how busy 2012 has been, she’ll do the same as Sharapova _ come into the U.S. Open not having played a competitive match since the Olympics.

Is this any way to prepare for her farewell?

“I remember 2009, I didn’t have many matches, either,” Clijsters said. “So I don’t worry about that.”