[1] Buică A, Llibre J.Averaging methods for finding periodic orbits via Brouwer degree. Bull Sci Math, 2004, 128: 7-22
[2] Buică A, Llibre J, Makarenkov O.Bifurcations from nondegenerate families of periodic solutions in Lipschitz systems. J Differential Equations, 2012, 252(6): 3899-3919
[3] Cândido M R, Llibre J, Novaes D D.Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction. Nonlinearity, 2017, 30: 3560-3586
[4] Chang X, Li Y.Rotating periodic solutions of second order dissipative dynamical systems. Discrete Contin Dyn Syst, 2016, 36: 643-652
[5] Cheng C, Huang F, Li Y.Affine-periodic solutions and pseudo affine-periodic solutions for differential equations with exponential dichotomy and exponential trichotomy. J Appl Anal Comput, 2016, 6: 950-967
[6] Ekeland I.Hamilton-Jacobi on the symplectic group. Rend Istit Mat Univ Trieste, 2017, 49: 137-146
[7] Evard J Cl, Jafari F.The set of all $m\times n$ rectangular real matrices of rank $r$ is connected by analytic regular arcs. Proc Amer Math Soc, 1994, 120: 413-419
[8] Giné J, Llibre J, Wu K, Zhang X.Averaging methods of arbitrary order, periodic solutions and integrability. J Differential Equations, 2016, 260: 4130-4156
[9] Hale J K. Ordinary Differential Equations.2nd ed. Huntington, NY: Robert E Krieger Publishing Co, Inc, 1980
[10] Han M, Sun H, Balanov Z.Upper estimates for the number of periodic solutions to multi-dimensional systems. J Differential Equations, 2019, 266: 8281-8293
[11] Hirsch M W. Differential Topology.Graduate Texts in Mathematics, No 33. New York, Heidelberg: Springer-Verlag, 1976
[12] Jiang X, Yang X, Li Y.Affine periodic solutions of stochastic differential equations. arXiv:1908.11499
[13] Krylov N, Bogolyubov N.Prilozhenie metodov nelineinoi mekhaniki k teorii statsionarnykh kolebanii (The Application of Methods of Nonlinear Mechanics to the Theory of Stationary oscillations). Kiev: Akademiya Nauk UkrainskoĭSSR, 1934
[14] Li Y, Huang F.Levinson's problem on affine-periodic solutions. Adv Nonlinear Stud, 2015, 15: 241-252
[15] Liang F, Han M, Jiang C.Limit cycle bifurcations of a planar near-integrable system with two small parameters. Acta Math Sci, 2021, 41B: 1034-1056
[16] Liu G, Li Y, Yang X.Existence and multiplicity of rotating periodic solutions for resonant Hamiltonian systems. J Differential Equations, 2018, 265: 1324-1352
[17] Liu G, Li Y, Yang X.Infinitely many rotating periodic solutions for second-order Hamiltonian systems. J Dyn Control Syst, 2019, 25: 159-174
[18] Liu G, Li Y, Yang X.Rotating periodic solutions for asymptotically linear second-order Hamiltonian systems with resonance at infinity. Math Methods Appl Sci, 2017, 40: 7139-7150
[19] Liu G, Li Y, Yang X.Rotating periodic solutions for super-linear second order Hamiltonian systems. Appl Math Lett, 2018, 79: 73-79
[20] Liu S, Han M, Li J.Bifurcation methods of periodic orbits for piecewise smooth systems. J Differential Equations, 2021, 275: 204-233
[21] Llibre J, Novaes D D.Improving the averaging theory for computing periodic solutions of the differential equations. Z Angew Math Phys, 2015, 66(4): 1401-1412
[22] Llibre J, Novaes D D, Teixeira M A.Higher order averaging theory for finding periodic solutions via Brouwer degree. Nonlinearity, 2014, 27: 563-583
[23] Moser J.Is the solar system stable? Math Intelligencer, 1978, 1(2): 65-71
[24] Novaes D D, Silva F B.Higher order analysis on the existence of periodic solutions in continuous differential equations via degree theory. SIAM J Math Anal, 2021, 53: 2476-2490
[25] Palais B, Palais R.Euler's fixed point theorem: the axis of a rotation. J Fixed Point Theory Appl, 2007, 2(2): 215-220
[26] Rhouma M B H, Chicone C. On the continuation of periodic orbits. Methods Appl Anal, 2000, 7(1): 85-104
[27] Sanders J, Verhulst F, Murdock J.Averaging Methods in Nonlinear Dynamical Systems. Applied Mathematical Sciences. New York: Springer, 2007
[28] Verhulst F.Nonlinear Differential Equations and Dynamical Systems. New York: Springer Science & Business Media, 2006
[29] Wang C, Yang X, Li Y.Affine-periodic solutions for nonlinear differential equation. Rocky Mountain J Math, 2016, 46: 1717-1737
[30] Wang H, Yang X, Li Y.Rotating-symmetric solutions for nonlinear systems with symmetry. Acta Math Appl Sin Engl Ser, 2015, 31: 307-312
[31] Wang S, Yang X, Li Y. The mechanism of rotating waves in a ring of unidirectionally coupled Lorenz systems. Commun Nonlinear Sci Numer Simul, 2020, 90: Art 105370
[32] Xing J, Yang X, Li Y.Affine-periodic solutions by averaging methods. Sci China Math, 2018, 61: 439-452
[33] Xing J, Yang X, Li Y.Lyapunov center theorem on rotating periodic orbits for Hamiltonian systems. J Differential Equations, 2023, 363: 170-194
[34] Xing J, Yang X, Li Y.Rotating periodic solutions for convex Hamiltonian systems. App Math Lett, 2019, 89: 91-96
[35] Xu F, Yang X.Affine-periodic solutions by asymptotic method. J Dyn Control Syst, 2021, 27: 271-281
[36] Xu F, Yang X, Li Y, Liu M.Existence of affine-periodic solutions to Newton affine-periodic systems. J Dyn Control Syst, 2019, 25: 1-19
[37] Yang X, Zhang Y, Li Y.Existence of rotating-periodic solutions for nonlinear systems via upper and lower solutions. Rocky Mountain J Math, 2017, 47: 2423-2438
[38] Zhang Y, Yang X, Li Y. Affine-periodic solutions for dissipative systems. Abstr Appl Anal, 2013, 2013: Art 157140
