In Galatians 1:16b-19, 22 (ESV), Paul writes that after his conversion in Damascus,
...I did not immediately consult with anyone; nor did I go up to Jerusalem to those who were apostles before me, but I went away into Arabia, and returned again to Damascus. Then after three years I went up to Jerusalem to visit Cephas and remained with him fifteen days. But I saw none of the other apostles except James the Lord's brother.... And I was still unknown in person to the churches of Judea that are in Christ.
However, the author of Acts describes the events of Paul's conversion in 9:1-19, and in describing the events which occurred immediately after (9:19b-20, 23-28, ESV), he writes concerning Paul:
For some days he was with the disciples at Damascus. And immediately he proclaimed Jesus in the synagogues, saying, "He is the Son of God." ... When many days had passed, the Jews plotted to kill him, but their plot became known to Saul. They were watching the gates day and night in order to kill him, but his disciples took him by night and let him down through an opening in the wall, lowering him in a basket. And when he had come to Jerusalem, he attempted to join the disciples. And they were all afraid of him, for they did not believe that he was a disciple. But Barnabas took him and brought him to the apostles and declared to them how on the road he had seen the Lord, who spoke to him, and how at Damascus he had preached boldly in the name of Jesus. So he went in and out among them at Jerusalem, preaching boldly in the name of the Lord.
According to the author of Acts, this is Paul's first trip to Jerusalem after his conversion in Damascus. The next trip Paul takes to Jerusalem according to his account in Galatians 2:1 (ESV) follows:
Then after fourteen years I went up again to Jerusalem with Barnabas, taking Titus along with me.
The next mention of Paul's location in the book of Acts is in 11:25-26b, which records:
So Barnabas went to Tarsus to look for Saul, and when he had found him, he brought him to Antioch.
This later trip to Jerusalem has already been dealt with in another question, I reference it only to make it clear that it is unlikely that there is another trip to Jerusalem that is being confused with this first post-conversion trip recorded in Galatians and Acts.
Obviously there are many differences in these accounts (did Paul go to Jerusalem to see Peter by his own choice or was he forced to flee there to escape persecution? Did he go to Arabia before Jerusalem or not? Did the other Christians take him away to Caesarea and then to Tarsus to protect him from the Hellenists, or did he return to the regions of Syria and Cilicia?). The primary difference I am interested in in this question is which apostles Paul saw in his first post-conversion trip to Jerusalem, but a good answer may need to address some or all of these other contradictory chronological statements in order to address this (if one makes the case that the chronology can be reconciled).
So in light of these texts and their presented chronology, which apostles did Paul visit in Jerusalem the first time he went there after his conversion? Was the author of Acts unaware of the letter to the Galatians? Did the author perhaps intentionally write a polemic to rebut/correct the Galatians account? How do esteemed Biblical scholars understand the differences between the accounts in these texts?