What was going on when I was born?

Prime Minister Zhao Ziyang today reiterated China's offer to let Taiwan retain its capitalist economic and social system if it reu nited with the Communist mainland. The renewed overture was linked to the initialing of an agreement on Hong Kong by Britain and China four days ago. That accord allows the territory to keep its free enterprise system and life style for 50 years after it is returned to Chinese rule in 1997. China has said that Taiwan could be a special administrative region like Hong Kong but could have even broader autonomy. The Chinese Government has asserted that Taiwan could keep its armed forces, while Chinese troops will be garrisoned in Hong Kong.

Take what they have left and what they have taught you with their dying and keep it with your own. . . And in that time when men decide and feel safe to call the war insane, take one moment to embrace those gentle heroes you left behind. . . The words were written in Vietnam 14 years ago by Maj. Michael Davis O'Donnell of Springfield, Ill., three months before he was lost when his helicopter was shot down. Now, the major's poem and the writings of other Vietnam veterans, their families and friends are being considered for inscription on a memorial planned for lower Manhattan. Page B1.

During the recession, the Eaton Corporation cut back the number of its business jets from seven to five. Now profits have rebounded at the auto industry supplier, but it has no plans to replace the planes. Similarly, the Ford Motor Company, which has a fleet of eight planes, has reduced the number of its pilots since 1979 from 27 to 23 and has put one plane on part-time use. It has decided to hold off replacing four turboprop planes and one Gulfstream II that date from the 1960's.

The candidate was asked why Walter F. Mondale would be more successful than Ronald Reagan in a parley with the Soviets. ''Lemme just put it to ya this way,'' Geraldine A. Ferraro began, in her finest oratorical style. Syntax and thoughts were flying, vowels were flattening and syllables were dropping. But the audience of Associated Press news executives in Providence, R.I., was listening raptly and admiringly, caught up in the tough and sassy Queens speaking style that has become the surprise hit of the campaign season.

NEW BRUNSWICK, N.J. The wait was over, the suspense had ended at last, and now the Rutgers football players had assembled to listen to their new head coach. As Dick Anderson stood before his players, he left them with an unmistakable first impression. What Albert Smith, the leading rusher for the last two seasons, remembered from that meeting had nothing to do with lofty goals or inspiring speeches. The memory he took from that day was an invitation for the players to remove their hats. It was once not uncommon to see a lot of hats in the team's dressing room; baseball hats, woolen hats, all kinds. ''He walked in and he said, 'Can you take your hats off?' '' Smith said. Somewhere in their coach's request - in his tall frame, the deep-set eyes, the voice a sergeant would like, or all those things - was the message: And keep them that way.

The Jets answered one question but created another today in their 28- 21 loss to the New England Patriots, a game in which three of their key performers were sidelined with injuries. Pat Ryan was able to move the offense when the running game broke down, but the defense allowed 354 passing yards as Tony Eason was protected so well that for the first time this season Mark Gastineau and the other defenders were unable to produce a sack. Halting Gastineau, the league- leader with nine sacks in the first four games, was so emotional for the right tackle Darryl Haley that he was unable to talk to the news media after the game about what he had accomplished. Lyons Angry Afterward Because Eason luxuriated in not being touched by a defender once during the game, he was able to pass for three touchdowns, including two in the third period that broke a 14-all tie. Eason's first start, against the Jets late last season, was different. In that game, he was sacked five times, three times by Gastineau.

New tax law provisions intended to identify abusive tax shelters and punish violators more severely are bolstering efforts by the Internal Revenue Service and the Justice Department to curb unwarranted deductions. The I.R.S. says the 1984 tax act, approved by Congress two months ago, is helping it to block shelters that are essentially tax dodges, lacking economic merit. It also reports that the courts are getting tougher and that the service's success rate in audits has improved markedly. The Justice Department's tax division, meanwhile, says it will have two dozen lawyers working exclusively on fraudulent shelters. A tax shelter, basically, is an investment that provides substantial deductions from income otherwise taxable to the investor. Real estate and oil exploration are two of the most popular. The Government regards as abusive the shelters that promise immediate deductions of several times the taxpayer's cash investment, especially if the venture seems to have little prospect of earning profits.

King Hussein of Jordan tonight defended his decision to restore full diplomatic relations with Egypt, and challenged Syria, Libya and other critics of his action to come to a summit meeting to debate this and other issues that have divided the Arabs. Earlier today, Syria rejected a call for a such a meeting. The King predicted that other Arab nations would ''inevitably'' restore full diplomatic relations with Egypt. In an interview at Nadwa Palace, the King asserted that Syria and Libya, but not Jordan, had repeatedly violated Arab summit resolutions by, among other things, supporting Iran in its war against Iraq, undermining Yasir Arafat, whom the King called the ''legitimate representative of the Palestine Liberation Organization,'' and by preventing Arab summit meetings from being held.

Just one week after being appointed chairman and chief executive of Walt Disney Productions, Michael D. Eisner moved to strengthen that beleaguered company's motion picture division. Mr. Eisner and Frank G. Wells, Disney's president and chief operating officer, announced today that they had named Jeffrey Katzenberg as Disney's president of motion pictures and television. Mr. Katzenberg, 33 years old, is president of movie production at Paramount Pictures. He is considered the hardest-working of Hollywood's younger production executives. At Disney, he will be responsible for all production, marketing and distribution.

New rules take effect today intended to streamline the process of writing commercial letters of credit, the principal means of payment in international trade. The new rules are a recognition of the increasing use of modern data transmission systems and office automation equipment. However, some experts fear that in making the writing of letters of credit simpler, the new rules could also open the door to more abuses. There is general agreement, though, that the first overhaul of standards in a decade was needed to update a system that has fostered trade for more than a thousand years.

MONDAY, OCTOBER 1, 1984 International Preliminary talks with Moscow on arms control and other issues are expected to begin within a few weeks as a result of conversations with Foreign Minister Andrei A. Gromyko, Reagan Administration officials said. But they said they doubted actual negotiations would resume before the end of this year or early next year. (Page A1, Column 6.) Jordan's renewal of ties with Egypt was defended by King Hussein. He challenged Syria, Libya and other critics of his decision to restore full diplomatic relations to come to a summit meeting to debate this and other issues that have divided Arab ranks. Syria turned down the King's invitation. (A1:2.)

Mike Witt, whose brief major league career has been dotted with many imperfections despite his talent, today became only the 13th pitcher in major league history to toss a perfect game when he pitched the California Angels to a 1-0 season-ending victory over the Texas Rangers. So overpowering was the 24-year- old right-hander that he allowed only four balls to be hit out of the infield. He struck out 10 in recording his second shutout and ninth complete game. Witt (15-11) threw only 94 pitches, 70 for strikes.