
<PAGE>   1

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CUSIP No. 00169100                       13G                       Page 51 of 54
- ------------------                                                 -------------



                                   Exhibit A

                             JOINT FILING AGREEMENT

         In accordance with Rule 13d-1(f) under the Securities Exchange Act of
1934, as amended, the undersigned hereby agree to the joint filing on behalf of
each of them of a statement on Schedule 13G (including amendments thereto) with
respect to the Common Stock of AMC Entertainment, Inc and that this Agreement be
included as an Exhibit to such statement.

         IN WITNESS WHEREOF, the undersigned hereby execute this Agreement
effective as of the 14th day of February, 2001.



Date:  February 14, 2001          Sandler Capital Management



                                  By:    /s/ MOIRA MITCHELL
                                     -----------------------------------------
                                  Name:  Moira Mitchell
                                     -----------------------------------------
                                  Title: President
                                     -----------------------------------------

Date:  February 14, 2001          Sandler Associates



                                  By:    /s/ EDWARD G. GRINACOFF
                                     -----------------------------------------
                                  Name:  Edward G. Grinacoff
                                     -----------------------------------------
                                  Title: General Partner
                                     -----------------------------------------

Date:  February 14, 2001          Sandler Mezzanine General Partnership



                                  By:     /s/ EDWARD G. GRINACOFF
                                     -----------------------------------------
                                  Name:   Edward G. Grinacoff
                                     -----------------------------------------
                                  Title:  Secretary
                                     -----------------------------------------

Date:  February 14, 2001          Sandler Mezzanine Partners, L.P.
                                  By:   Sandler Mezzanine General Partnership,
                                        its General Partner
                                        By: MJM Media Corp.,
                                            a General Partner

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CUSIP No. 00169100                       13G                       Page 52 of 54
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Date:  February 14, 2001          Sandler Mezzanine T-E Partners, L.P.



                                  By:  /s/ EDWARD G. GRINACOFF
                                      -----------------------------------------
                                  Name: Edward G. Grinacoff
                                     -----------------------------------------
                                  Title: Secretary
                                     -----------------------------------------

Date:  February 14, 2001          Sandler Mezzanine Foreign Partners, L.P.



                                  By: /s/ EDWARD G. GRINACOFF
                                     -----------------------------------------
                                  Name: Edward G. Grinacoff
                                     -----------------------------------------
                                  Title: Secretary
                                     -----------------------------------------

Date:  February 14, 2001          Sandler Communications Offshore Fund, Inc.



                                  By: /s/ EDWARD G. GRINACOFF
                                     -----------------------------------------
                                  Name: Edward G. Grinacoff
                                     -----------------------------------------
                                  Title: Director
                                     -----------------------------------------

Date:  February 14, 2001          ARPH Media Corp.



                                  By: /s/ EDWARD G. GRINACOFF
                                     -----------------------------------------
                                  Name: Edward G. Grinacoff
                                     -----------------------------------------
                                  Title: Secretary
                                     -----------------------------------------



<PAGE>   3

- ------------------
CUSIP No. 00169100                       13G
- ------------------


Date:  February 14, 2001         Kornreich Media Corp.



                                  By:    /s/ EDWARD G. GRINACOFF
                                     -----------------------------------------
                                  Name:  Edward G. Grinacoff
                                     -----------------------------------------
                                  Title: Secretary
                                     -----------------------------------------

Date:  February 14, 2001         MJM Media Corp.



                                  By:    /s/ EDWARD G. GRINACOFF
                                     -----------------------------------------
                                  Name:  Edward G. Grinacoff
                                     -----------------------------------------
                                  Title: Secretary
                                     -----------------------------------------


Date:  February 14, 2001         ARH Corp.



                                  By:    /s/ MOIRA MITCHELL
                                     -----------------------------------------
                                  Name:  Moira Mitchell
                                     -----------------------------------------
                                  Title: Secretary
                                     -----------------------------------------

Date:  February 14, 2001         MJDM Corp.



                                  By:    /s/ MOIRA MITCHELL
                                     -----------------------------------------
                                  Name:  Moira Mitchell
                                     -----------------------------------------
                                  Title: President
                                     -----------------------------------------


Date:  February 14, 2001         Four JK Corp.



                                  By:    /s/ MOIRA MITCHELL
                                     -----------------------------------------
                                  Name:  Moira Mitchell
                                     -----------------------------------------
                                  Title: President
                                     -----------------------------------------


Date:  February 14, 2001         By:   /s/ HARVEY SANDLER
                                     -----------------------------------------
                                  Name:  Harvey Sandler


<PAGE>   4

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CUSIP No. 00169100                       13G                       Page 54 of 54
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Date:  February 14, 2001          By:    /s/ PHYLLIS SANDLER
                                     -----------------------------------------
                                  Name:  Phyllis Sandler


Date:  February 14, 2001          By:    /s/ MICHAEL J. MAROCCO
                                     -----------------------------------------
                                  Name:  Michael J. Marocco


Date:  February 14, 2001          By:    /s/ EDWARD G. GRINACOFF
                                     -----------------------------------------
                                  Name:  Edward G. Grinacoff


Date:  February 14, 2001          By:    /s/ ANDREW SANDLER
                                     -----------------------------------------
                                  Name:  Andrew Sandler


Date:  February 14, 2001          By:    /s/ DOUGLAS E. SCHIMMEL
                                     -----------------------------------------
                                  Name:  Douglas E. Schimmel


Date:  February 14, 2001          By:    /s/ MICHELE C. SCHIMMEL
                                     -----------------------------------------
                                  Name:  Michele C. Schimmel


Date:  February 14, 2001          By:    /s/ DAVID LEE
                                     -----------------------------------------
                                  Name:  David Lee


Date:  February 14, 2001          By:    /s/ HANNAH STONE
                                     -----------------------------------------
                                  Name:  Hannah Stone


