Este trabajo estudia el comportamiento dinámico de las soluciones positivas de la ecuación en diferencias , donde , y son números reales positivos, y las condiciones iniciales son números positivos arbitrarios. Establecemos algunos resultados sobre la estabilidad y carácter de oscilación de esta ecuación para .

God of Our Fathers (arr. W. Smith for choir, percussion and brass ensemble) (02 min. 16 sec.) / Warren -- Bless This House (02 min. 43 sec.) / Brahe -- Rock of Ages (arr. A. Harris for choir, brass ensemble and percussion) (03 min. 34 sec.) / Hastings -- Alleluia! Sing to Jesus! (arr. A. Newman for brass ensemble) (02 min. 32 sec.) / Prichard -- Ellens Gesang III (Ave Maria!), Op. 52, No. 6, D. 839, "Hymne an die Jungfrau" (arr. R.R. Bennett for choir, organ and orchestra) (05 min. 04 sec.) / Schubert -- Fairest Lord Jesus (02 min. 28 sec.) / -- O God, Our Help in Ages Past (arr. A. Newman for brass ensemble) (01 min. 10 sec.) / Croft -- Amazing Grace (02 min. 36 sec.) / -- The Old Rugged Cross (02 min. 30 sec.) / Bennard -- Prayer of Thanksgiving (arr. R. Cundick and E. Kremser for choir and 2 organs) (02 min. 45 sec.) / -- In the Garden (02 min. 16 sec.) / Miles -- Lead, Kindly Light (03 min. 48 sec.) / Dykes -- The Holy City (arr. R.R. Bennett for choir, organ and orchestra) (06 min. 21 sec.) / Adams -- A Mighty Fortress Is Our God (arr. A. Newman for brass ensemble) (02 min. 42 sec.) / Luther -- The Church's one foundation (02 min. 11 sec.) / Wesley -- Holy, holy, holy! (arr. A. Newman for brass ensemble) (01 min. 48 sec.) / Dykes -- Onward, Christian Soldiers (arr. A. Harris for choir, percussion and brass ensemble) (03 min. 04 sec.) / Sullivan -- Blessed Assurance (02 min. 28 sec.) / Knapp -- Come, Come Ye Saints (arr. L. Robertson for choir and orchestra) (06 min. 02 sec.) / -- Pass Me Not, O Gentle Saviour (02 min. 43 sec.) / Doane -- Crown Him with Many Crowns (arr. A. Newman for brass ensemble) (01 min. 44 sec.) / Thring -- Ave Maria (arr. R. Hayman for voice and orchestra) (02 min. 55 sec.) / Bach -- Joyful, Joyful, We Adore Thee (arr. A. Newman for brass ensemble) (01 min. 40 sec.) / Beethoven -- How Great Thou Art (arr. S.K. Hine for choir) (02 min. 53 sec.) / -- The Lord's Prayer (arr. P.J. Wilhousky for choir and orchestra) (03 min. 14 sec.) / Malotte

La lune est coustumiere (04 min. 18 sec.) / Clereau -- Quand j'étais libre (02 min. 27 sec.) / Chardavoine -- Revecy venir du printemps (03 min. 48 sec.) / Le Jeune -- Que n'est elle aupres de moy (02 min. 19 sec.) / Certon -- La plus des plus (07 min. 47 sec.) / Josquin des Prez -- Il viendra le jour desire (02 min. 29 sec.) / La Rue -- La Nuit froide et sombre (02 min. 22 sec.) / Lassus -- Quand je congneu en ma pensee (01 min. 41 sec.) / Sandrin -- Quand j'estois libre (03 min. 01 sec.) / Chardavoine -- Missa plurium modulorum: Jouyssance vous donneray (02 min. 42 sec.) / Sermisy -- O doulx regard (02 min. 59 sec.) / Janequin -- Amour, Amour donne moy paix ou treve (03 min. 58 sec.) / Caietin -- Helas ma Dame (01 min. 48 sec.) / Hesdin -- Fiere cruelle en amour (04 min. 15 sec.) / Le Jeune -- J'en ay dueil (07 min. 38 sec.) / Ockeghem -- Mon coeur se recommande (02 min. 15 sec.) / Lassus -- Airs a 3, 4, 5 et 6 parties: L'un apreste la glu (04 min. 09 sec.) / Le Jeune -- Quand j'estois libre (02 min. 22 sec.) / Chardavoine -- Secoures-moy, ma dame (05 min. 27 sec.) / Sermisy -- Se congie prens (03 min. 55 sec.) / Josquin des Prez -- Cueurs desolenz (02 min. 18 sec.) / Josquin des Prez

Morerna i Spanien, eller Barndomens valde (The Moors in Spain, or Childhood's Choices): Overture (02 min. 38 sec.) / Eggert -- II. Marche: Grave (03 min. 21 sec.) / Eggert -- III. Fugue: Adagio maestoso - Allegro (04 min. 32 sec.) / Eggert -- I. Adagio maestoso - Allegro spirito (13 min. 08 sec.) / Eggert -- Marche (01 min. 25 sec.) / Eggert -- Entr'acte between Acts I and II (02 min. 02 sec.) / Eggert -- Act II: Postlude (NaN min. NaN sec.)(53 sec.) / Eggert -- Entr'acte between Acts II and III (02 min. 21 sec.) / Eggert -- Act III: Prelude: Marche (01 min. 15 sec.) / Eggert -- Marche and Chorale (03 min. 56 sec.) / Eggert -- Entr'acte between Acts III and IV (01 min. 13 sec.) / Eggert -- Entr'acte between Acts IV and V (01 min. 09 sec.) / Eggert -- IV. Finale: Allegro vivace (07 min. 26 sec.) / Eggert -- III. Minuet and Trio: Allegro (03 min. 38 sec.) / Eggert -- II. Andante (06 min. 08 sec.) / Eggert -- I. Adagio mesto - Allegro con brio (10 min. 53 sec.) / Eggert

6 Songs, Op. 48: No. 4. Die Ehre Gottes aus der Natur (arr. F. Mottl for choir and orchestra) (02 min. 44 sec.) / Beethoven -- Transeamus usque Bethlehem (02 min. 58 sec.) / Schnabel -- Ellens Gesang III (Ave Maria!), Op. 52, No. 6, D. 839, "Hymne an die Jungfrau (version for choir) (04 min. 24 sec.) / Schubert -- Deutsche Messe, D. 872: Heilig, heilig, heilig (03 min. 48 sec.) / Schubert -- Ave Maria (03 min. 16 sec.) / Bach -- Ave Maria, WAB 6 (04 min. 04 sec.) / Bruckner -- Agnus Dei (arr. H. Baumann for choir and orchestra) (03 min. 23 sec.) / Bizet -- Deutsche Messe, D. 872: Zum Gloria: Ehre, Ehre sei Gott in der Hohe (03 min. 27 sec.) / Schubert -- Messiah, HWV 56, Part II: Hallelujah (04 min. 16 sec.) / Handel -- Mass in B Minor, BWV 232: Gloria in excelsis Deo (06 min. 52 sec.) / Bach -- Kyrie in B-Flat Major, D. 45 (02 min. 14 sec.) / Schubert -- Salve regina in B-Flat Major, D. 386 (03 min. 48 sec.) / Schubert -- Die Schöpfung (The Creation), Hob.XXI:2: Die Himmel erzahlen die Ehre Gottes (04 min. 03 sec.) / Haydn -- Mass No. 10 in C Major, Hob.XXII:9, "Missa in tempore belli", "Paukenmesse", "Kriegsmesse": Gloria: Gloria in excelsis Deo (02 min. 49 sec.) / Haydn -- Ein deutsches Requiem (A German Requiem), Op. 45: II. Denn alles Fleisch es ist wie Gras (05 min. 27 sec.) / Brahms

Ave Maria (arr. M. Maisky for cello and piano) (05 min. 30 sec.) / Bach -- Violin Sonata in D Major, Op. 1, No. 13, HWV 371: III. Larghetto (arr. M. Maisky for cello and piano) (03 min. 23 sec.) / Handel -- Les ballets du roi: Gavotte (arr. for cello and piano) (02 min. 50 sec.) / Lully -- Orfeo ed Euridice, Act II: Dance of the Blessed Spirits, "Melodie" (arr. for cello and piano) (03 min. 49 sec.) / Gluck -- Lied ohne Worte (Song without Words), Op. 109, MWV Q34 (04 min. 57 sec.) / Mendelssohn -- 24 Preludes, Op. 28: No. 6 in B Minor (arr. for cello and piano) (02 min. 31 sec.) / Chopin -- Ellens Gesang III (Ave Maria!), Op. 52, No. 6, D. 839, "Hymne an die Jungfrau (arr. J. Palaschko for cello and piano) (05 min. 35 sec.) / Schubert -- Kinderszenen (Scenes of Childhood), Op. 15: No. 7. Träumerei (Dreaming) (arr. for cello and piano) (03 min. 46 sec.) / Schumann -- 5 Lieder in Op. 49: No. 4. Wiegenlied (arr. M. Maisky for cello and piano) (02 min. 28 sec.) / Brahms -- 7 Canciones populares españolas: No. 5. Nana (arr. M. Maisky for cello and piano) (03 min. 04 sec.) / Falla -- 3 Songs, Op. 7: No. 1. Après un rêve (arr. M. Maisky for cello and piano) (03 min. 25 sec.) / Fauré -- Les Erinnyes: Élégie (arr. M. Maisky for cello and piano) (02 min. 28 sec.) / Massenet -- Le carnaval des animaux: XII. Le Cygne (The Swan) (version for cello and piano) (03 min. 34 sec.) / Saint-Saëns -- Piece en forme de habanera: Vocalise-etude en forme de habanera (arr. P. Bazelaire for cello and piano) (03 min. 44 sec.) / Ravel -- Catalan Folksong (arr. P. Casals for cello and piano) (03 min. 12 sec.) / -- 6 Morceaux, Op. 19: No. 4. Nocturne (version for cello and piano) (05 min. 01 sec.) / Tchaikovsky -- 14 Songs, Op. 34: No. 14. Vocalise (arr. L. Rose for cello and piano) (07 min. 05 sec.) / Rachmaninov -- Liebesleid (arr. M. Maisky for cello and piano) (03 min. 53 sec.) / Kreisler

Ellens Gesang III (Ave Maria!), Op. 52, No. 6, D. 839, "Hymne an die Jungfrau" (04 min. 56 sec.) / Schubert -- Cantique de Noël (O Holy Night) (Sung in French) (arr. A. Kremski for voice and orchestra) (04 min. 57 sec.) / Adam -- Panis angelicus (04 min. 01 sec.) / Franck -- Ave Maria (03 min. NaN sec.) / Bach -- La salutation angelique (03 min. 49 sec.) / Gounod -- Grande messe des morts, Op. 5, "Requiem": Sanctus (10 min. 16 sec.) / Berlioz -- Panis Angelicus (03 min. 27 sec.) / Saint-Saëns -- O Divine Redeemer, "Repentir" (05 min. 26 sec.) / Gounod -- Crucifix (03 min. 25 sec.) / Faure -- Messe solennelle de Sainte Cecile: Sanctus (06 min. 15 sec.) / Gounod -- Agnus Dei (04 min. 48 sec.) / Bizet -- Notre Pere (02 min. 36 sec.) / Alagna -- Stille Nacht (Silent Night) (04 min. 31 sec.) / Gruber -- Adeste fideles (O Come All Ye Faithful) (02 min. 23 sec.) / Wade -- Gentil pere Noel (02 min. 32 sec.) / Alagna -- Petit Papa Noel (arr. D. Alagna and F. Alagna for voice, choir and orchestra) (04 min. 32 sec.) / Martinet -- Notre Pere (05 min. 09 sec.) / Alagna -- Panis angelicus (03 min. 44 sec.) / Franck

La plus que lente (arr. L. Roques for violin and piano) (04 min. 21 sec.) / Debussy -- Violin Partita No. 3 in E Major, BWV 1006: IV. Menuett I-II (arr. for violin and piano) (02 min. 25 sec.) / Bach -- Pieces de clavecin, Book 3: 17th Ordre in E Minor: Les petits moulins a vent (arr. M. Press for violin and piano) (01 min. NaN sec.) / Couperin -- Preludes, Book 1: No. 8. La fille aux cheveux de lin (The Girl with the Flaxen Hair) (arr. A. Hartmann for violin and piano) (02 min. 29 sec.) / Debussy -- Stimmungen (Moods), Op. 73: No. 2. Scherzo-Impromptu (arr. J. Achron for violin and piano) (02 min. 15 sec.) / Grieg -- Hebrew Melody, Op. 33 (arr. L. Auer for violin and piano) (04 min. 56 sec.) / Achron -- Piano Sonata No. 17 in D Major, Op. 53, D. 850, "Gasteiner Sonate": IV. Rondo: Allegro moderato (arr. C. Friedberg for violin and piano) (04 min. 49 sec.) / Schubert -- Ellens Gesang III (Ave Maria!), Op. 52, No. 6, D. 839, "Hymne an die Jungfrau" (arr. A. Wilhelmj for violin and piano) (05 min. 04 sec.) / Schubert -- Spanish Dances, Op. 23: No. 2. Zapateado (03 min. 24 sec.) / Sarasate -- Estrellita (arr. J. Heifetz for violin and piano) (02 min. 52 sec.) / Ponce -- 7 Canciones populares españolas: No. 4. Jota (arr. P. Kochanski for violin and piano) (02 min. 42 sec.) / Falla -- Lyric Pieces, Book 10, Op. 71: No. 3. Puck: No. 3. Puck (arr. J. Achron for violin and piano) (NaN min. NaN sec.)(55 sec.) / Grieg -- 6 Gesänge, Op. 34: No. 2. Auf Flugeln des (arr. J. Achron and J. Heifetz for violin and piano) (03 min. 33 sec.) / Heifetz -- Violin Sonata No. 3 in C Minor, Op. 45: II. Allegretto espressivo alla romanza (04 min. 43 sec.) / Grieg -- Valse bluette, "Air de ballet No. 2" (arr. L. Auer for violin and piano) (01 min. 48 sec.) / Drigo -- Rondo in E-Flat Major, Op. 11, "Rondo favori" (arr. J. Heifetz for violin and piano) (04 min. 34 sec.) / Hummel -- Sea Murmurs (arr. J. Heifetz for violin and piano) (01 min. 26 sec.) / Castelnuovo-Tedesco -- Tale of Tsar Saltan, Op. 57: Flight of the Bumble-bee (arr. J. Heifetz for violin and piano) (01 min. 15 sec.) / Rimsky-Korsakov -- 4 Impromptus, Op. 90, D. 899: No. 3 in G-Flat Major (arr. J. Heifetz for violin and piano) (04 min. 14 sec.) / Schubert -- English Suite No. 3 in G Minor, BWV 808: IV. Sarabande (arr. J. Heifetz for violin and piano) (03 min. 11 sec.) / Bach -- Alt Wien (Old Vienna) (arr. J. Heifetz for violin and piano) (02 min. 42 sec.) / Godowsky -- 4 Pieces from Much Ado about Nothing, Op. 11: II. Holzapfel und Schlehwein (02 min. 12 sec.) / Korngold -- Tzigane (07 min. 47 sec.) / Ravel -- Largo in C Minor (arr. G. Dandelot for violin and piano) (03 min. 58 sec.) / Clérambault -- Suite española No. 1, Op. 47: III. Sevilla (Sevillanas) (arr. J. Heifetz for violin and piano) (03 min. 55 sec.) / Albéniz -- L'enfant prodigue: Prelude (arr. J. Heifetz for violin and piano) (02 min. 42 sec.) / Debussy -- Ruralia hungarica, Op. 32a: VI. Andante (arr. F. Kreisler for violin and piano) (04 min. 34 sec.) / Dohnányi -- La capricieuse, Op. 17 (03 min. 25 sec.) / Elgar -- Saudades do Brasil, Op. 67b: IX. Sumare (arr. C. Levy for violin and piano) (01 min. 58 sec.) / Milhaud -- I. Preludio (NaN min. NaN sec.)(39 sec.) / Vivaldi -- II. Capriccio (NaN min. NaN sec.)(45 sec.) / Vivaldi -- III. Corrente (01 min. 23 sec.) / Vivaldi -- IV. Recitativo (01 min. 23 sec.) / Vivaldi -- V. Giga (01 min. 45 sec.) / Vivaldi -- I. Allegro aperto - Adagio - Allegro aperto (09 min. 54 sec.) / Mozart -- II. Adagio (10 min. 49 sec.) / Mozart -- III. Tempo di menuetto (06 min. 38 sec.) / Mozart -- 24 Caprices, Op. 1: No. 13 in B-Flat Major (arr. F. Kreisler for violin and piano) (03 min. 15 sec.) / Paganini -- V. Gavotte I (01 min. 33 sec.) / Bach -- VI. Gavotte II (01 min. 41 sec.) / Bach -- 24 Caprices, Op. 1: No. 24 in A Minor (arr. L. Auer for violin and piano) (07 min. 25 sec.) / Paganini -- Stimmungsbilder, Op. 9, TrV 127: No. 2. An einsamer Quelle (arr. J. Heifetz for violin and piano) (03 min. 41 sec.) / Strauss -- Guitarre, Op. 45, No. 2 (arr. P. Sarasate for violin and piano) (03 min. 04 sec.) / Moszkowski -- Alt Wien, Op. 30 (arr. for violin and piano) (03 min. 02 sec.) / Castelnuovo-Tedesco -- Scherzo-tarantelle, Op. 16 (04 min. 19 sec.) / Wieniawski

4 Impromptus, Op. 90, D. 899: No. 3 in G-Flat Major (06 min. 49 sec.) / Schubert -- Divertissement sur des motifs originaux francais, D. 823: No. 2. Andantino varie in B Minor, Op. 84, No. 1 (01 min. 03 sec.) / Schubert -- 16 German Dances and 2 Ecossaises, Op. 33, D. 783: German Dance No. 5 in B Minor (NaN min. NaN sec.)(41 sec.) / Schubert -- Ungarische Melodie, D. 817 (03 min. 14 sec.) / Schubert -- 12 Valses Nobles, Op. 77, D. 969: Valse No. 10 in F Major (NaN min. NaN sec.)(43 sec.) / Schubert -- Waltz in G-Flat Major, D. Anh. I/14, "Kupelwieser-Walzer" (01 min. 44 sec.) / Schubert -- Ellens Gesang III (Ave Maria!), Op. 52, No. 6, D. 839, "Hymne an die Jungfrau" (arr. for cello and piano) (04 min. 44 sec.) / Schubert -- Du bist die Ruh, Op. 59, No. 3, D. 776 (arr. for cello and piano) (04 min. 11 sec.) / Schubert -- Piano Quintet in A Major, Op. 114, D. 667, "Die Forelle" (The Trout): IV. Tema con variazioni (07 min. 28 sec.) / Schubert -- 16 German Dances and 2 Ecossaises, Op. 33, D. 783: German Dance No. 10 in A Minor (01 min. 18 sec.) / Schubert -- Fantasie in F Minor, Op. 103, D. 940: Allegro molto moderato (05 min. 19 sec.) / Schubert -- Piano Trio No. 2 in E-Flat Major, Op. 100, D. 929: II. Andante con moto (09 min. 16 sec.) / Schubert -- 38 Walzer, Ländler und Ecossaisen (38 Waltzes, Ländler and Ecossaises), Op. 18, D. 145: Waltz No. 8 (NaN min. NaN sec.)(46 sec.) / Schubert -- Piano Sonata No. 20 in A Major, D. 959: II. Andantino (03 min. 07 sec.) / Schubert -- 34 Valses Sentimentales, Op. 50, D. 779: Valse No. 13 in A Major (01 min. 15 sec.) / Schubert -- Arpeggione Sonata in A Minor, D. 821, "Arpeggione": II. Adagio (arr. for cello and piano) (04 min. 07 sec.) / Schubert -- Octet in F Major, Op. 166, D. 803: IV. Thema: Andante (05 min. 29 sec.) / Schubert

La Wally, Act I: Ebben? Ne andro lontana (04 min. 04 sec.) / Catalani -- Rinaldo, Act II: Lascia ch'io pianga (04 min. 24 sec.) / Handel -- Don Giovanni, K. 527, Act II: Vedrai, carino (03 min. 27 sec.) / Mozart -- The Bohemian Girl: I Dreamt I Dwelt in Marble Halls (04 min. 10 sec.) / Balfe -- Giuditta: Meine Lippen, sie kussen so heiss (04 min. 57 sec.) / Lehár -- Anna Magdalena Notenbuch (Clavier-Buchlein III): Bist du bei mir, BWV 508 (attrib. G.H. Stolzel) (02 min. 44 sec.) / Bach -- Messiah, HWV 56, Part I: Aria: Rejoice greatly, O daughter of Zion (04 min. 16 sec.) / Handel -- Ellens Gesang III (Ave Maria!), Op. 52, No. 6, D. 839, "Hymne an die Jungfrau" (version for voice and orchestra) (03 min. 58 sec.) / Schubert -- Melodies of the Heart, Op. 5: No. 3. Ich liebe dich (Jeg elsker dig) (02 min. 31 sec.) / Grieg -- Morgen, Op. 27, No. 4 (03 min. 45 sec.) / Strauss -- Chants d'Auvergne, Vol. 3: No. 4. Brezairola (Cradle Song) (03 min. 40 sec.) / Canteloube -- 5 Lieder, Op. 49: No. 4. Wiegenlied (02 min. 01 sec.) / Brahms -- Carmina Burana: In trutina (02 min. 07 sec.) / Orff -- Cuatro madrigales amatorios: De los alamos vengo, madre (02 min. 09 sec.) / Rodrigo -- Die lustige Witwe (The Merry Widow): Vilia (04 min. 56 sec.) -- The Dancing Years: Waltz Of My Heart (02 min. 41 sec.) / Novello -- Conversation Piece: I'll follow my secret heart (04 min. 21 sec.) / Coward -- I'll walk beside you (02 min. 30 sec.) / Murray -- Abide with me (02 min. 59 sec.) / Monk -- Down by the Sally gardens (02 min. 24 sec.) / -- Greensleeves (03 min. 49 sec.) / -- Old American Songs, Set I: III. Long time ago (02 min. 37 sec.) -- The King and I: Something Wonderful (03 min. 05 sec.) / Rodgers