Can I safely connect the headphone output from my iPad or iPhone to the "AUX" input of my car stereo?

If the music plays on the device, it should play on your car stereo via an auxillary cable with no difficulty. See here

Yes; that is the purpose if the AUX input. If you use a cable that only connects the audio output to the AUX input, you will have to control the music from your iPod.

I would imagine so… Aux is Aux! I plug my iPod into the Aux jack on my home stereo as well as in my car, using a cable that I bought from Radio Shack for about $6.

Of course. That’s the whole point of AUX.

It works but it’s not ideal. I would use the USB instead.

The JVC player may even control the iPod (show song titles, for example) depending on the model.

But the headphone jack works, too. With most music and certainly in a car you won’t hear the difference.

A headphone signal is tuned a bit differently than the line out signal which AUX is designed for.

Using the headphone-jack-to-aux, turn the iPod volume low. Headphone output is higher than line in, and the higher volume can distort the sound.

Oh, I totally missed that the stereo has USB! I would try to connect the iPod that way, since you could then use the car stereo to control the iPod.

Thank you all for your help.
OK, yes, I do understand that AUX is for input to the car stereo from external devices. I was concerned about compatibility, amperage and voltage-wise. For example, wall chargers for the iPhone output 1A, but the iPad requires a charger that outputs 2.1A. I didn’t know if there were similar issues here with playing music, and didn’t want to blow anything out.
@jaytkay Thanks for the warning about volume. I understand that AUX is for input only, but USB is both input and output, is that correct?

Yes, USB is two-way, input and output.

If your car stereo can control the iPod, it sends signals to the iPod – Play, Choose Song, Forward, Back etc.

And the Ipod sends music to the car stereo.