Sharkovsky ordering / / Alexander M. Blokh and Oleksandr M. Sharkovsky

• Record Nr.: UNISA996490347503316
• Autore: Blokh Alexander M. <1958->
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 3-030-99125-3
• Descrizione fisica: 1 online resource (114 pages)
• Collana: SpringerBriefs in mathematics
• Disciplina: 514.322
• Soggetti: Combinatorial dynamics; Differential equations; Dynamics - Mathematics; Dinàmica combinatòria; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Coexistence of Cycles for Continuous Interval Maps -- 1.1 Introduction -- 1.2 Proof of Forcing Sh-Theorem -- 1.2.1 Loops of Intervals Force Periodic Orbits -- 1.2.2 The Beginning of the Sh-order -- 1.2.3 Three Implies Everything -- 1.2.4 Minimal Cycles Imply Sh-weaker Periods -- 1.2.5 Orbits with Sh-strongest Periods Form Simplest Cycles -- 1.3 Proof of Realization Sh-Theorem -- 1.4 Stability of the Sh-ordering -- 1.5 Visualization of the Sh-ordering -- References -- 2 Combinatorial Dynamics on the Interval -- 2.1 Introduction -- 2.2 Permutations: Refinement of Cycles' Coexistence -- 2.3 Rotation Theory -- 2.4 Coexistence of Homoclinic Trajectories and Stratification of the Space of Maps -- 2.4.1 Homoclinic Trajectories, Horseshoes, and L-Schemes -- 2.4.2 Coexistence (of Homoclinic Trajectories) and Its Stability: Powers of Maps with L-Scheme and Homoclinic Trajectories -- References -- 3 Coexistence of Cycles for One-Dimensional Spaces -- 3.1 Circle Maps -- 3.2 Maps of the nn-od -- 3.3 Other Graph Maps -- 3.3.1 Graph-Realizable Sets of Periods -- 3.3.2 Trees -- 3.3.3 Graphs With Exactly One Loop -- 3.3.4 Figure Eight Graph -- References -- 4 Multidimensional Dynamical ; Systems -- 4.1 Triangular Maps -- 4.2 Cyclically Permuting Maps -- 4.3 Multidimensional Perturbations of One-Dimensional Maps -- 4.4 Infinitely-Dimensional Dynamical Systems, Generated by One-Dimensional Maps -- 4.5 Final Remarks -- 4.5.1 Multivalued Maps -- 4.5.2 Nonlinear Difference Equations -- References -- 5 Historical Remarks -- Appendix Appendix -- A.1 The Copy of the First Page of the Paper From 1964 -- A.2 The Copy of the Last Page of the Paper From 1964 -- A.3 Translation of the Original Paper From 1964.