One part of the divided Korean Peninsula is paralyzed by frenzied mourning of a leader it deified. The other is shrugging its shoulders, hoping that in the aftermath of Kim Jong Il’s death, nothing too bad will happen.

Kim’s body was presented to a grieving North Korea on Tuesday, ensconced in a glass case and surrounded by rows of the official state flower, the Kimjongilia. The deep-red blossoms matched the blanket that covered Kim from the chest down. His head rested atop a pillow.

The late dictator’s youngest son, heir-apparent Kim Jong Eun, paid his respects before the cameras while thousands of North Koreans wept in public squares.

“I feel heartbroken,” one middle-aged woman told Pyongyang’s state-run media.

For South Koreans, Kim’s unexpected death drove home an unsettling disparity between them and their neighbors — a gap that could spark turmoil should an unstable North Korea collapse. At this point, some in Seoul say, North and South Korea hold nothing in common but a language.

Decades ago, the two shared a common history, with millions in each country holding memories of the Korean War. But now, only the oldest generations can clearly recall life before the partition. Sentiment in South Korea has shifted slowly against unification, as a younger generation fears the economic havoc it could wreak.

North Korea has turned increasingly inscrutable, the result of Kim’s isolationist policies and, more recently, conservative South Korean President Lee Myung-bak’s retreat from most intra-Korean relations.

Although the North idealized Kim before and during his 17-year rule, Koreans in the South derided him. For the past two days, as the high-definition televisions that are ubiquitous in this uber-wired country have transmitted otherworldly images of grief from across the border, South Korean flags remained at full staff.

People finished their Christmas shopping. Eighty-year-old Seoul resident Kim Dae-jong, who was born in North Korea, spent Tuesday morning surfing the Internet — and tried not to think too much about his sister, who is still living in the North.

“I’m 100 percent sure that I won’t be able to see my home town again in my lifetime,” he said.

With Kim Jong Il’s death, that divide carries fresh consequences, analysts in Seoul say. If Kim Jong Eun, thought to be in his late 20s, struggles to consolidate his power in Pyongyang, nuclear-armed North Korea could lose grasp of its rigid social control, throwing the region into chaos.

Even if his transition is smooth, how he would govern is hard to predict, given the secrecy of North Korea’s power circle.

Pyongyang announced Kim’s death at noon on Monday, about 52 hours after he had a heart attack. Not even the barest rumors leaked out in the interim. Seoul’s intelligence chief learned the news as most others here did: on television.

South Korea’s government expressed condolences Tuesday to the North Korean people but said it won’t send an official delegation to the Dec. 28 funeral.

Some Koreans said they worry about tension escalating on the peninsula. But those who are older than 30 remember the unexpected death in 1994 of North Korea founder Kim Il Sung, a moment when many experts predicted the Stalinist nation’s swift demise. As it turned out, Kim’s son, Kim Jong Il, rose to power and held the country intact through repressive tactics and an all-consuming personality cult.

By the end of the decade, the two Koreas had entered the most peaceful 10-year period of coexistence in their modern history.

“So I would describe the general mood here as subdued,” said John Delury, an assistant professor at Seoul’s Yonsei University. “Seoul is not in a state of alert.”

For now, North Korea has shown no signs of turmoil. The Associated Press, with a reporter in Pyongyang, described “somber streets” with no discord.

The state-controlled media have spent two days paying homage to Kim Jong Eun, calling him a “great person born of heaven” — a description previously used for his father and grandfather. The Korean Central News Agency said that North Koreans would trust and follow Kim Jong Eun “under whatever circumstances.”

In recent years, though, economic hardships and food shortages in the North have pushed more and more defectors into the South. Almost a year ago, the 20,000th defector arrived.

The newcomers usually struggle to adjust, with an unemployment rate three times as high as that of the rest of the population. Just two in five say they “feel welcome” in South Korea, according to one survey.

On Monday morning, defector Park Choong-sik, 27, headed to Sogang University, on the northern side of Seoul, to work on a documentary exploring defectors’ adjustments to a democratic society.

He met a 30-year-old college student who had fled North Korea only five years earlier. The college student said he was doing well; he even introduced Park to several of his friends.

Just as they were about to film, Park received a phone call.

Kim had died.

Park, who had left North Korea in 1997, stomped his feet and threw up his hands.

“I was exhilarated,” he later said.

But the other, more recent defector grew quiet, concerned. And his South Korean-born friends didn’t seem to care much.

Park contemplated canceling the shoot. But he stayed, attending a lecture, following the recent defector to a library and later conducting an interview.

“Yeah, Kim Jong Il had died,” Park said, “but we agreed that we should continue our work.”

Special correspondent Yoonjung Seo contributed to this report.