LEADER 01826nam0 2200373 i 450 001 SUN0127047 005 20200302091943.399 010 $d0.00 017 70$2N$a978-3-030-16833-9 100 $a20200220d2019 |0engc50 ba 101 $aeng 102 $aCH 105 $a|||| ||||| 200 1 $a*New Trends in One-Dimensional Dynamics$eIn Honour of Welington de Melo on the Occasion of His 70th Birthday IMPA 2016, Rio de Janeiro, Brazil, November 14?17$fMaria José Pacifico, Pablo Guarino editors 205 $aCham : Springer, 2019 210 $aviii$d333 p.$cill. ; 24 cm 215 $aPubblicazione in formato elettronico 410 1$1001SUN0102574$12001 $a*Springer proceedings in mathematics & statistics$v285$1210 $aBerlin$cSpringer$d2012-. 606 $a37Fxx$xDynamical systems over complex numbers [MSC 2020]$2MF$3SUNC020362 606 $a37Axx$xErgodic theory [MSC 2020]$2MF$3SUNC021388 606 $a37Cxx$xSmooth dynamical systems: general theory [MSC 2020]$2MF$3SUNC021948 606 $a37Dxx$xDynamical systems with hyperbolic behavior [MSC 2020]$2MF$3SUNC021949 606 $a37Exx$xLow-dimensional dynamical systems [MSC 2020]$2MF$3SUNC022337 620 $aCH$dCham$3SUNL001889 702 1$aPacifico$b, Maria José$3SUNV098468 702 1$aGuarino$b, Pablo$3SUNV098469 712 12$aNew Trends in One-dimensional Dynamics meeting$f2016$eRio de Janeiro$3SUNV098470 712 $aSpringer$3SUNV000178$4650 801 $aIT$bSOL$c20210503$gRICA 856 4 $uhttp://doi.org/10.1007/978-3-030-16833-9 912 $aSUN0127047 950 $aUFFICIO DI BIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08CONS e-book 1681 $e08eMF1681 20200220 996 $aNew Trends in One-Dimensional Dynamics$91732606 997 $aUNICAMPANIA LEADER 04296nam 22007215 450 001 9910978380703321 005 20250212115412.0 010 $a9783031628108 010 $a3031628101 024 7 $a10.1007/978-3-031-62810-8 035 $a(CKB)37515644400041 035 $a(MiAaPQ)EBC31903254 035 $a(Au-PeEL)EBL31903254 035 $a(OCoLC)1499354023 035 $a(DE-He213)978-3-031-62810-8 035 $a(EXLCZ)9937515644400041 100 $a20250212d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTwo-dimensional Crossing-Variable Cubic Nonlinear Systems /$fby Albert C. J. Luo 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (338 pages) 311 08$a9783031628092 311 08$a3031628098 327 $aConstant and crossing-cubic vector fields -- Crossing-linear and crossing-cubic vector fields -- Crossing-quadratic and crossing-cubic Vector Field -- Two crossing-cubic vector fields. 330 $aThis book is the fourth of 15 related monographs presents systematically a theory of crossing-cubic nonlinear systems. In this treatment, at least one vector field is crossing-cubic, and the other vector field can be constant, crossing-linear, crossing-quadratic, and crossing-cubic. For constant vector fields, the dynamical systems possess 1-dimensional flows, such as parabola and inflection flows plus third-order parabola flows. For crossing-linear and crossing-cubic systems, the dynamical systems possess saddle and center equilibriums, parabola-saddles, third-order centers and saddles (i.e, (3rd UP+:UP+)-saddle and (3rdUP-:UP-)-saddle) and third-order centers (i.e., (3rd DP+:DP-)-center, (3rd DP-, DP+)-center) . For crossing-quadratic and crossing-cubic systems, in addition to the first and third-order saddles and centers plus parabola-saddles, there are (3:2)parabola-saddle and double-inflection saddles, and for the two crossing-cubic systems, (3:3)-saddles and centers exist. Finally, the homoclinic orbits with centers can be formed, and the corresponding homoclinic networks of centers and saddles exist. Readers will learn new concepts, theory, phenomena, and analytic techniques, including · Constant and crossing-cubic systems · Crossing-linear and crossing-cubic systems · Crossing-quadratic and crossing-cubic systems · Crossing-cubic and crossing-cubic systems · Appearing and switching bifurcations · Third-order centers and saddles · Parabola-saddles and inflection-saddles · Homoclinic-orbit network with centers · Appearing bifurcations Develops equilibrium singularity and bifurcations in 2-dimensional self-cubic systems; Presents (1,3) and (3,3)-sink, source, and saddles; (1,2) and (3,2)-saddle-sink and saddle-source; (2,2)-double-saddles; Develops homoclinic networks of source, sink and saddles. 606 $aPlasma waves 606 $aMultibody systems 606 $aVibration 606 $aMechanics, Applied 606 $aDynamics 606 $aNonlinear theories 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aWaves, instabilities and nonlinear plasma dynamics 606 $aMultibody Systems and Mechanical Vibrations 606 $aApplied Dynamical Systems 606 $aMathematical and Computational Engineering Applications 615 0$aPlasma waves. 615 0$aMultibody systems. 615 0$aVibration. 615 0$aMechanics, Applied. 615 0$aDynamics. 615 0$aNonlinear theories. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 14$aWaves, instabilities and nonlinear plasma dynamics. 615 24$aMultibody Systems and Mechanical Vibrations. 615 24$aApplied Dynamical Systems. 615 24$aMathematical and Computational Engineering Applications. 676 $a530.44 700 $aLuo$b Albert C. J$0720985 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910978380703321 996 $aTwo-Dimensional Crossing-Variable Cubic Nonlinear Systems$94323204 997 $aUNINA