Dynamic page in WordPress site

You could make your own shortcode, say [mypage]. To make this work, you will need to add some code to functions.php:

<?php
  add_shortcode('mypage', 'mypagefunction');
  function mypagefunction() {
    $html = 'statements to do whatever';
    return $html;
  } // end function

Best to do this with a child theme to avoid your work being overwritten by updates.

Alternatively, you could make your own custom page template. Start with an existing one and modify it to suit.