L5

L5_01_Introduction to bifurcations

L5_02_Why important?

L5_03_Implicit function theorem, assumptions

L5_04_Implicit function theorem, conclusions

L5_05_Implicit function theorem, illustration

L5_06_Implicit function theorem, formulas

L5_07_Assumptions for no additional fixed points

L5_08_Concusions, no additional fixed points

L5_09_Justifiction, no additional fixed points

L5_10_Assumptions, no additional periodic orbits

L5_11_Conclusions, no additional periodic orbits

L5_12_Proof, no additional periodic orbits

L5_13_Non bifurcations and general conclusion

L5_14_Saddle node assumptions

L5_15_Saddle node conclusions (known mistake: The branches u>0 and uu_0 and u

L5_16_Saddle node proof first assertion

L5_17_Saddle node proof remaining assertions

L5_18_Period doubling assumptions

L5_19_Period doubling conclusions

L5_20_The non-zero speed condition

L5_21_Four szenarios

L5_22_The proof idea

L5_23_Transcritical assumptions

L5_24_Transcritical conclusions

L5_25_Transcritical comments

L5_26_Pitchfork assumptions

L5_27_Pitchfork conclusions

L5_28_Szenarios and genericity

L5_29_A never ending story