In the sardonic Israeli film “Broken Wings,” a grieving, sleepwalking family stubbornly refuses to wake up to reality — until it’s forced to.

Numbly stumbling through their chaotic routine, the traumatized Ullman clan is on the precipice of either reinvention or collapse. Either they’ll snap out of their funk, or disaster will overtake them. What’s certain, though, is that the current state of affairs can’t endure much longer.

The great accomplishment of writer-director Nir Bergman, making his feature debut, is delicately pitching the film so as to sustain the equal likelihood of impending doom or droll survival for the longest possible time. At the same time, by striking a cautiously hopeful tone tinged with dark humor, Bergman effectively inoculates his drama against the viruses of despair and sentimentality.

The plot, approach and themes of “Broken Wings” will not be unfamiliar to fans of American independent movies such as “Welcome to the Dollhouse” or “Pieces of April.” That the film collected a remarkable nine Israeli Academy Awards, however, suggests that it was viewed at home as a kind of harbinger of a new Israeli cinema.

Set in a distinctly unglamorous section of Haifa, where Bergman grew up, “Broken Wings” essays a portrait of an exhausted single mother, Dafna (played by veteran stage actress Orly Silbersatz-Banai), trying to manage four children while working a hospital midwife’s crazy hours.

The burden, inevitably, falls on the oldest child, 17-year-old Maya (Maya Maron, in a heart-tugging performance), who’d much rather be living her life than baby-sitting her siblings. But when Dafna gets stuck late at work, she calls Maya on her cell phone to instruct her to hustle home — even if it means the teenage goth princess has to abandon her band mates just before they take the stage for a high-profile Battle of the Bands show.

It’s an enormous sacrifice, for which Maya may never forgive Dafna. Needless to say, it’s neither the first nor last time that Maya’s asked to play surrogate mom. As soon becomes clear, the daughter-mother relationship is at the core of the movie.

Maya is permanently ticked off at her nihilistic brother Yair, who’s just a year younger but has dropped out of school and sleeps most of the day. He’s not a bad guy, but he can’t be bothered to raise a finger to help.

The youngest, and most helpless, siblings are Ido, an 11-year-old boy who’s the bullies’ favorite target at school, and his 6-year-old sister, Bahr.

All the children are shortchanged when it comes to Dafna’s attention and guidance, so Maya is hardly singled out. But because she’s reached the age where she can recognize what she needs — and what she lacks — we feel her frustration most acutely.

In a singularly deft touch, Bergman waits an hour into the film before letting us know what set the Ullmans on their current course. We can’t help but surmise or guess until then, filling in our own explanation for the troubled family dynamic.

Despite its angst and pain, “Broken Wings” is neither an angry nor subversive film. Teen sex, marijuana, rock ‘n’ roll posters and T-shirts are all on display, but they don’t symbolize the decline of Western civilization.

Rather, the movie suggests, growing up is always about clamoring for attention, testing limits and, as in Maya’s case, seeking out the things — like affection and recognition — that you can’t get at home.

Driven by a genuine fondness for its stubbornly self-centered characters, the likable and persuasive “Broken Wings” heralds the arrival of an unusually intriguing young filmmaker.

“Broken Wings” opens Friday, April 30, at the UA Galaxy, 1285 Sutter St., S.F.; the Act One/Act Two, 2128 Center St., Berkeley; and the Camera 3, 288 S. Second St., San Jose; and Friday, May 7, at the Rafael Film Center, 1118 Fourth St., San Rafael.