The film helped bring breaking into the mainstream. Over the years, it also became famous for the subs and doubles of its star, Jennifer Beals.At the climax of a strip routine, a young woman in silhouette arches back across a chair and pulls a cord. A cascade of water drenches her flexed body.In a leotard and leg warmers, the same woman stretches and runs in place, her wet hair flinging moisture as she shakes and rolls her head.Still in the leotard and leg warmers, she faces a panel of judges at an audition— jog-skipping while pumping her arms high, turning and turning, diving into a somersault, spinning her on back.These and other moments from the 1983 movie “Flashdance” still circulate in cultural memory, loved and mocked and recognized, even by people who never saw the film. On Monday, in honor of its 40th anniversary, New Yorkers get a rare chance to watch it on a big screen, as the closing selection of this year’s Dance on Camera Festival at Film at Lincoln Center. Get ready to cheer or jeer.Jennifer Beals, the star of “Flashdance,” in the off-the-shoulder sweatshirt she made famous.Everett Collection“So many people hold it in a special place,” Michael Trusnovec, a curator of the festival, said, noting how the movie’s style permeated the Long Island dance studios that he grew up in. He also pointed to how “Flashdance” had affected fashion: the sweatshirts with the neck hole cut to fall off one shoulder. And he stressed how dancers, including those inspired by the brief appearance of B-boys, had gravitated to the movie, thinking: “That’s what I want to do. I want to be that.”Beyond dance, much of the movie’s staying power comes from the soundtrack, especially Michael Sembello’s “Maniac” and Giorgio Moroder’s “What a Feeling,” sung by Irene Cara. The songs support sequences that are essentially music videos, which is how those scenes (the jogging workout, the audition) became ubiquitous on MTV — and why they still circulate online. Cara’s voice connects “Flashdance” to “Fame,” the 1980 movie with her hit title song, just as the supporting actress Cynthia Rhodes connects it to “Dirty Dancing,” from 1987. It’s an ’80s dance-film node.Beals in the movie’s freak-out scene.Paramount Pictures, via Getty ImagesThere’s some fondness for the plot, too. Set in Pittsburgh, it’s a follow-your-dreams story and a Cinderella tale. Alex — Jennifer Beals in the role that made her a star — is a welder by day and dances in a burlesque club at night (occasioning not just the famous water-drenched number but also a freak-out in white Kabuki makeup amid strobe lights). Her dream is to be accepted into a prestigious dance conservatory. By the end, she gets in, and she gets the guy, her older boss at the steel mill.Over the years, the film has acquired a kind of notoriety, too, because Beals did so little of Alex’s dancing. Most was performed by a French dancer, Marine Jahan. And in the climactic audition scene, there were more doubles: the gymnast Sharon Shapiro for the dive into the roll; and for the backspin, the 16-year-old B-boy Richard Colon, better known as Crazy Legs.Richard Colon, better known as Crazy Legs, doubling for Beals.Paramount Pictures, via Getty ImagesInitially, Colon said in an interview, he was brought in to teach the other doubles — on the day before shooting. That wasn’t enough time, so the director, Adrian Lyne, asked him to perform the backspin himself, in a leotard and wig, after shaving his legs and his newly grown mustache.“I was this little arrogant Puerto Rican from the Bronx with all this machismo,” Colon said. “I put my hands up to Lyne’s face and rubbed my fingers together, like, ‘You gotta pay me.’”They paid enough, Colon said. And in the next decades, the residual checks “definitely came in handy,” he added, as did his joke about being the first in hip-hop to dress in drag.Colon was known to the filmmakers because he was already in the movie. He and a few other members of the pioneering B-boy group Rock Steady Crew appear in another scene, when Alex discovers them dancing with a boombox on the sidewalk.To the B-boy anthem “It’s Just Begun” by the Jimmy Castor Bunch, Normski pops and locks like a windup robot, Ken Swift and Crazy Legs spin on their backs and Mr. Freeze holds an umbrella while doing the backslide, just before Michael Jackson made that decades-old move famous as the Moonwalk. This one-minute sequence had an outsized impact.“It’s impossible to overestimate the significance of ‘Flashdance’ in the history of breaking,” said Joseph Schloss, the author of “Foundation: B-boys, B-girls and Hip-Hop Culture in New York.” “That one scene pretty much single-handedly brought breaking into the mainstream.”Some members of Rock Steady were at first hesitant to be in the movie. “We didn’t practice with other groups,” Colon said, “because it was all about the element of surprise.” Marc Lemberger, better known as Mr. Freeze, said he was afraid that other dancers would “bite our moves”— steal them.A scene from “Flashdance.”Parmount PicturesAfter the movie’s release, the crew “became instant ghetto celebrities,” Colon said. “There was lots of love and lots of jealousy.” They got on the David Letterman show and into “Beat Street,” one of a few breaking-themed movies that came out the next year. “Flashdance” is connected to that part of the ’80s, too.The Hollywood interest was a quick fad, but breaking lived on. For decades, Colon said, he would meet people who sneaked into “Flashdance” just to see that one scene, people who saw themselves in the dance, many of them far from the Bronx.“When you talk to people in different hip-hop dance scenes around the world,” Schloss said, “almost inevitably they will say, ‘Well, the first time we saw it was in ‘Flashdance.’”In “Planet B-boy,” a 2008 documentary focused on the international B-boy competition Battle of the Year, dancers from Japan, Germany and France all testify to that effect. (And where did the director of the film, Benson Lee, get idea for the documentary? From rewatching “Flashdance” and wondering what had happened to the form.)The ripples from the scene can also be felt in “Top Nine,” a new documentary getting its world premiere at Dance on Camera just before “Flashdance.” It’s about the Russian B-boy crew Top 9, formed around 20 years ago.Its members tell their story of banding together, improving their skills and gaining global respect for Russian B-boys. They win Battle of Year in 2008, beating a dominant Korean crew. That glory doesn’t solve their money problems — this isn’t a “Flashdance” fairy tale — but they keep dancing.Through it all, they don’t mention “Flashdance,” but listen to the song they use to win in 2008: “It’s Just Begun.” And when some of them start a festival in St. Petersburg, which masters do they import? Ken Swift and Crazy Legs. More