LEADER 03624nam 2200589 450 001 9910480769303321 005 20170821170702.0 010 $a1-4704-0651-9 035 $a(CKB)3360000000464428 035 $a(EBL)3113520 035 $a(SSID)ssj0000889163 035 $a(PQKBManifestationID)11478250 035 $a(PQKBTitleCode)TC0000889163 035 $a(PQKBWorkID)10876424 035 $a(PQKB)10587551 035 $a(MiAaPQ)EBC3113520 035 $a(PPN)195411277 035 $a(EXLCZ)993360000000464428 100 $a19810424h19811981 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aQualitative analysis of the periodically forced relaxation oscillations /$fMark Levi 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[1981] 210 4$dİ1981 215 $a1 online resource (163 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 244 300 $a"Volume 32, number 244 (first of 3 numbers)." 311 $a0-8218-2244-6 320 $aBibliography: pages 146-147. 327 $a""Table of Contents""; ""A?1. Introduction""; ""1.1. A short history of the problem""; ""1.2. Classical results""; ""1.3. Later developments""; ""1.4. Some questions posed by the classical results""; ""1.5. Outline of the paper""; ""A?2. Results""; ""2.1. Geometry of Poincare map (the main result)""; ""2.2. Qualitative analysis of the equation-results""; ""2.3. An informal explanation of the shape of Poincare map; geometry of Levinson's results""; ""A. Global behaviour of the phase flow""; ""B. Geometry of Levinson's results""; ""C. An application to the large amplitude case"" 327 $a""2.4. A family of annulus maps""""A. An example of a family of annulus maps""; ""B. Projected circle maps; notations""; ""C. Hypothesis""; ""D. Analysis of the map""; ""A?3. Proof of the Hypothesis for an equation of van der Pol type""; ""3.0. Statement of the main result""; ""3.1. Construction of the window map""; ""A. Factorization""; ""B. Construction of the window r""; ""3.2. Global behaviour of the solutions; Linearized and Hessian systems""; ""A. Behaviour of the solutions""; ""B. Linearized and Hessian systems""; ""3.3. Deformation of the window r with the flow"" 327 $a""3.4. Proof of H1 """"3.5. Proof of H2""; ""3.6. Nondegeneracy of the homoclinic tangency""; ""A?4. Qualitative analysis of the equation a??? proof of Theorem 2.2""; ""Appendix to A?2.4. a??? Proof of Theorem 2.3""; ""Appendix to A?3.1""; ""A. Two auxiliary lemmas""; ""B. Proof of Proposition 3.1""; ""C. Proof of Proposition 3.2""; ""D. Proof of the auxiliary lemmas""; ""Appendix to A?3.2""; ""A. Proof of theorem 3.2""; ""B. Proof of Lemmas 3.2 a??? 3.6""; ""Appendix to A?3.4. a??? Proof of Proposition 3.4""; ""A. Connection between f[sub(I??)] and g[sub(I??)]""; ""B. Proof of Proposition 3.4"" 327 $a""C. Proofs of Lemmas A3.4 a??? 1,2,3""""References"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 244. 606 $aDifferentiable dynamical systems 606 $aOscillations 608 $aElectronic books. 615 0$aDifferentiable dynamical systems. 615 0$aOscillations. 676 $a510 s 676 $a514/.74 700 $aLevi$b Mark$f1951-$0772034 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480769303321 996 $aQualitative analysis of the periodically forced relaxation oscillations$92470536 997 $aUNINA