LEADER 03409nam 2200529 450 001 9910591033503321 005 20230726173651.0 010 $a3-030-99125-3 035 $a(MiAaPQ)EBC7080724 035 $a(Au-PeEL)EBL7080724 035 $a(CKB)24782713200041 035 $a(PPN)264955579 035 $a(EXLCZ)9924782713200041 100 $a20230202d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSharkovsky ordering /$fAlexander M. Blokh and Oleksandr M. Sharkovsky 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (114 pages) 225 1 $aSpringerBriefs in mathematics 311 08$aPrint version: Blokh, Alexander M. Sharkovsky Ordering Cham : Springer International Publishing AG,c2022 9783030991234 320 $aIncludes bibliographical references. 327 $aIntro -- Preface -- Contents -- 1 Coexistence of Cycles for Continuous Interval Maps -- 1.1 Introduction -- 1.2 Proof of Forcing Sh-Theorem -- 1.2.1 Loops of Intervals Force Periodic Orbits -- 1.2.2 The Beginning of the Sh-order -- 1.2.3 Three Implies Everything -- 1.2.4 Minimal Cycles Imply Sh-weaker Periods -- 1.2.5 Orbits with Sh-strongest Periods Form Simplest Cycles -- 1.3 Proof of Realization Sh-Theorem -- 1.4 Stability of the Sh-ordering -- 1.5 Visualization of the Sh-ordering -- References -- 2 Combinatorial Dynamics on the Interval -- 2.1 Introduction -- 2.2 Permutations: Refinement of Cycles' Coexistence -- 2.3 Rotation Theory -- 2.4 Coexistence of Homoclinic Trajectories and Stratification of the Space of Maps -- 2.4.1 Homoclinic Trajectories, Horseshoes, and L-Schemes -- 2.4.2 Coexistence (of Homoclinic Trajectories) and Its Stability: Powers of Maps with L-Scheme and Homoclinic Trajectories -- References -- 3 Coexistence of Cycles for One-Dimensional Spaces -- 3.1 Circle Maps -- 3.2 Maps of the nn-od -- 3.3 Other Graph Maps -- 3.3.1 Graph-Realizable Sets of Periods -- 3.3.2 Trees -- 3.3.3 Graphs With Exactly One Loop -- 3.3.4 Figure Eight Graph -- References -- 4 Multidimensional Dynamical Systems -- 4.1 Triangular Maps -- 4.2 Cyclically Permuting Maps -- 4.3 Multidimensional Perturbations of One-Dimensional Maps -- 4.4 Infinitely-Dimensional Dynamical Systems, Generated by One-Dimensional Maps -- 4.5 Final Remarks -- 4.5.1 Multivalued Maps -- 4.5.2 Nonlinear Difference Equations -- References -- 5 Historical Remarks -- Appendix Appendix -- A.1 The Copy of the First Page of the Paper From 1964 -- A.2 The Copy of the Last Page of the Paper From 1964 -- A.3 Translation of the Original Paper From 1964. 410 0$aSpringerBriefs in mathematics. 606 $aCombinatorial dynamics 606 $aDifferential equations 606 $aDynamics$xMathematics 606 $aDinàmica combinatòria$2thub 608 $aLlibres electrònics$2thub 615 0$aCombinatorial dynamics. 615 0$aDifferential equations. 615 0$aDynamics$xMathematics. 615 7$aDinàmica combinatòria 676 $a514.322 700 $aBlokh$b Alexander M.$f1958-$01154927 702 $aSharkovsky$b Oleksandr M. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910591033503321 996 $aSharkovsky ordering$93005041 997 $aUNINA