Question: This ancient city of Cappadocia was named for a member of the Julio-Claudian dynasty wo was the son of who?

Context paragraphs:
Ariarathes VIII of Cappadocia: Ariarathes VIII Epiphanes (Ancient Greek: Ἀριαράθης Ἐπιφανής , Ariaráthēs Epiphanḗs; reigned c. 101–c. 96 BC and in 95 BC), King of Cappadocia, was the second son of Ariarathes VI of Cappadocia and wife Laodice of Cappadocia.  Ariarathes VIII had an older sister called Nysa and an older brother called Ariarathes VII of Cappadocia.

Julia (gens): The gens Julia or Iulia was one of the most ancient patrician families at Ancient Rome.  Members of the "gens" attained the highest dignities of the state in the earliest times of the Republic.  The first of the family to obtain the consulship was Gaius Julius Iulus in 489 BC.  The gens is perhaps best known, however, for Gaius Julius Caesar, the dictator, and grand uncle of the emperor Augustus, through whom the name was passed to the so-called Julio-Claudian dynasty of the 1st century AD.  The "nomen Julius" became very common in imperial times, as the descendants of persons enrolled as citizens under the early emperors began to make their mark in history.

Ancient City Ruins of Liye: The site of Ancient City Ruins of Liye () is the archaeological site of seat of the historic Qianling County () in Dongting Prefecture (), Qin dynasty (221 BC–206 BC).  Its site is located in the present-day Liye Town, Longshan County, Hunan Province, China, and it is known for 37,400 pieces of Qin Bamboo slips unearthed in 2002.  The Ancient City was built by Chu State in the late Warring States period, reconstructed in the Qin dynasty and abandoned in the early Western Han dynasty.  The site of Ancient City Ruins was approved as a hiistorical and cultural site protected at the national level in Hunan on November 22, 2002.  The Qin Bamboo Slips Museum and the Ruins Park has been established and officially opened on October 28, 2010.

Faustinopolis: Faustinopolis (also Colonia Faustinopolis and Halala) (Greek: Φαυστινόπολις ), was an ancient city in the south of Cappadocia, about 20 km south of Tyana.  It was named after the empress Faustina, the wife of Marcus Aurelius, who died there in a village, which her husband, by establishing a colony in it, raised to the rank of a town under the name of Faustinopolis.  Hierocles assigns the place to Cappadocia Secunda, and it is mentioned also in the Antonine and Jerusalem Itineraries.  The town was close to the defiles of the Cilician Gates, and was likely situated at modern-day Toraman, Niğde Province, Turkey.  Following the Muslim conquests and the subsequent Arab raids, the site was abandoned for the nearby fortress of Loulon.

Drusus Caesar: Drusus Caesar (Latin: "Drusus Iulius Caesar Germanicus" , AD 7 – AD 33) was a member of the Julio-Claudian dynasty in the early first century AD.  He was the second son of Germanicus and Agrippina the Elder.  After the death of his cousin Drusus the Younger in AD 23, he and his brother Nero were promoted by the emperor Tiberius as his heirs.  Their progression would be short lived: in AD 29, the feud between his family and the powerful Praetorian Prefect Sejanus led to their downfall.  First, his mother and Nero were exiled, and later Drusus was imprisoned in AD 30.  Their deaths allowed Germanicus' third son, Caligula, to become Rome's third emperor following the death of Tiberius in 37.

Claudius: Claudius ( ; Latin: "Tiberius Claudius Caesar Augustus Germanicus" ; 1 August 10 BC – 13 October 54 AD) was Roman emperor from 41 to 54.  A member of the Julio-Claudian dynasty, he was the son of Drusus and Antonia Minor.  He was born at Lugdunum in Gaul, the first (and until Trajan, the only) Roman Emperor to be born outside Italy.  Because he was afflicted with a limp and slight deafness due to sickness at a young age, his family ostracized him and excluded him from public office until his consulship, shared with his nephew Caligula in 37.

History of the Roman Empire: The history of the Roman Empire covers the history of Ancient Rome from the fall of the Roman Republic in 27 BC until the abdication of the last Western emperor in 476 AD.  Rome had begun expanding shortly after the founding of the Republic in the 6th century BC, though it did not expand outside of the Italian Peninsula until the 3rd century BC.  Civil war engulfed the Roman state in the mid 1st century BC, first between Julius Caesar and Pompey, and finally between Octavian and Mark Antony.  Antony was defeated at the Battle of Actium in 31 BC.  In 27 BC the Senate and People of Rome made Octavian "imperator" ("commander") thus beginning the Principate, the first epoch of Roman imperial history usually dated from 27 BC to 284 AD; they later awarded him the name Augustus, "the venerated".  The success of Augustus in establishing principles of dynastic succession was limited by his outliving a number of talented potential heirs: the Julio-Claudian dynasty lasted for four more emperors—Tiberius, Caligula, Claudius, and Nero—before it yielded in 69 AD to the strife-torn Year of Four Emperors, from which Vespasian emerged as victor.  Vespasian became the founder of the brief Flavian dynasty, to be followed by the Nerva–Antonine dynasty which produced the "Five Good Emperors": Nerva, Trajan, Hadrian, Antoninus Pius and the philosophically inclined Marcus Aurelius.  In the view of the Greek historian Dio Cassius, a contemporary observer, the accession of the emperor Commodus in 180 AD marked the descent "from a kingdom of gold to one of rust and iron"—a famous comment which has led some historians, notably Edward Gibbon, to take Commodus' reign as the beginning of the decline of the Roman Empire.

Claudiopolis (Cappadocia): Claudiopolis (Greek: Κλαυδιόπολις , "city of Claudius") was an ancient city of Cappadocia mentioned by Pliny (v. 24).  From its name one can adduce that it was named for Roman emperor Claudius.

Women in ancient Rome: Freeborn women in ancient Rome were citizens ("cives"), but could not vote or hold political office.  Because of their limited public role, women are named less frequently than men by Roman historians.  But while Roman women held no direct political power, those from wealthy or powerful families could and did exert influence through private negotiations.  Exceptional women who left an undeniable mark on history range from Lucretia and Claudia Quinta, whose stories took on mythic significance; fierce Republican-era women such as Cornelia, mother of the Gracchi, and Fulvia, who commanded an army and issued coins bearing her image; women of the Julio-Claudian dynasty, most prominently Livia (58 BC-AD 29), who contributed to the formation of Imperial "mores"; and the empress Helena ( 250-330 AD), a driving force in promoting Christianity.

Ariarathes VII of Cappadocia: Ariarathes VII Philometor ("mother-loving") (Ancient Greek: Ἀριαράθης Φιλομήτωρ , Ariaráthēs Philomḗtōr; reigned in 116–101 BC or 111–100 BC), King of Cappadocia, was the first son of King Ariarathes VI of Cappadocia and his wife Laodice of Cappadocia.  Ariarathes VII had an older sister called Nysa and a younger brother called Ariarathes VIII of Cappadocia.

Supporting paragraphs: Claudiopolis (Cappadocia) Claudius
Answer: Drusus and Antonia Minor