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Continuation and bifurcation of multisymmetric solutions in reversible Hamiltonian systems
On Poisson's statedependent delay
1.  Mathematisches Institut, Universität Gießen, Arndtstr. 2, D 35392 Gießen, Germany 
References:
[1] 
O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel and H. O. Walther, "Delay Equations: Functional, Complex and Nonlinear Analysis," Springer, New York, 1995. 
[2] 
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations," Springer, New York, 1993. 
[3] 
F. Hartung, Linearized stability for a class of neutral functional differential equations with statedependent delays, Journal of Nonlinear Analysis: Theory, Methods and Applications, 69 (2008), 16291643. 
[4] 
F. Hartung, T. Krisztin, H. O. Walther and J. H. Wu, Functional differential equations with statedependent delays: Theory and applications, in "Handbook of Differential Equations: Ordinary Differential Equations," Vol. III, 435545, Elsevier/NorthHolland, Amsterdam, 2006. 
[5] 
M. C. Irwin, "Smooth Dynamical Systems," Academic Press, London, 1980. 
[6] 
M. C. Mackey, Commodity price fluctuations:pricedependent delays and nonlinearities as explanatory factors, J. Economic Theory, 48 (1989), 497509. 
[7]  
[8] 
S. D. Poisson, Sur les équations auxdifférences melées, Journal de l'Ecole Polytechnique, Tome, VI (1806), 126147. 
[9] 
H. O. Walther, The solution manifold and $C^1$smoothness of solution operators for differential equations with statedependent delay, J. Differential Eqs., 195 (2003), 4665. doi: 10.1016/j.jde.2003.07.001. 
[10] 
H. O. Walther, Smoothness properties of semiflows for differential equations with state dependent delay, in "Proceedings of the International Conference on Differential and Functional Differential Equations, Moscow, 2002," 1 (2002), 4055, Moscow State Aviation Institute (MAI), Moscow 2003, English version: Journal of the Mathematical Sciences, 124 (2004), 51935207. doi: 10.1023/B:JOTH.0000047253.23098.12. 
[11] 
H. O. Walther, Algebraicdelay differential systems, statedependent delay, and temporal orderof reactions, J. Dynamics and Differential Eqs., 21 (2009), 195232. doi: 10.1007/s1088400991296. 
[12] 
H. O. Walther, Semiflows for neutral equations with statedependent delays, Fields Inst. Communications, to appear. 
[13] 
H. O. Walther, Linearized stability for semiflows generated by a class of neutral equations, with applications to statedependent delays, Journal of Dynamics and Differential Equations, 22 (2010), 439462. doi: 10.1007/s108840109168z. 
[14] 
H. O. Walther, Differential equations with locally bounded delay, J. Differential Equations, 252 (2012), 30013039. 
show all references
References:
[1] 
O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel and H. O. Walther, "Delay Equations: Functional, Complex and Nonlinear Analysis," Springer, New York, 1995. 
[2] 
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations," Springer, New York, 1993. 
[3] 
F. Hartung, Linearized stability for a class of neutral functional differential equations with statedependent delays, Journal of Nonlinear Analysis: Theory, Methods and Applications, 69 (2008), 16291643. 
[4] 
F. Hartung, T. Krisztin, H. O. Walther and J. H. Wu, Functional differential equations with statedependent delays: Theory and applications, in "Handbook of Differential Equations: Ordinary Differential Equations," Vol. III, 435545, Elsevier/NorthHolland, Amsterdam, 2006. 
[5] 
M. C. Irwin, "Smooth Dynamical Systems," Academic Press, London, 1980. 
[6] 
M. C. Mackey, Commodity price fluctuations:pricedependent delays and nonlinearities as explanatory factors, J. Economic Theory, 48 (1989), 497509. 
[7]  
[8] 
S. D. Poisson, Sur les équations auxdifférences melées, Journal de l'Ecole Polytechnique, Tome, VI (1806), 126147. 
[9] 
H. O. Walther, The solution manifold and $C^1$smoothness of solution operators for differential equations with statedependent delay, J. Differential Eqs., 195 (2003), 4665. doi: 10.1016/j.jde.2003.07.001. 
[10] 
H. O. Walther, Smoothness properties of semiflows for differential equations with state dependent delay, in "Proceedings of the International Conference on Differential and Functional Differential Equations, Moscow, 2002," 1 (2002), 4055, Moscow State Aviation Institute (MAI), Moscow 2003, English version: Journal of the Mathematical Sciences, 124 (2004), 51935207. doi: 10.1023/B:JOTH.0000047253.23098.12. 
[11] 
H. O. Walther, Algebraicdelay differential systems, statedependent delay, and temporal orderof reactions, J. Dynamics and Differential Eqs., 21 (2009), 195232. doi: 10.1007/s1088400991296. 
[12] 
H. O. Walther, Semiflows for neutral equations with statedependent delays, Fields Inst. Communications, to appear. 
[13] 
H. O. Walther, Linearized stability for semiflows generated by a class of neutral equations, with applications to statedependent delays, Journal of Dynamics and Differential Equations, 22 (2010), 439462. doi: 10.1007/s108840109168z. 
[14] 
H. O. Walther, Differential equations with locally bounded delay, J. Differential Equations, 252 (2012), 30013039. 
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