Формулы ляпуновской размерности аттракторов Хенона и Лоренца
Г. А. Леонов

Эта публикация цитируется в следующих статьяx:

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5. Leonov G.A., “Lyapunov Functions in the Global Analysis of Chaotic Systems”, Ukr. Math. J., 70:1 (2018), 42–66        
6. Gao W., Yan L., Saeedi M., Nik H.S., “Ultimate Bound Estimation Set and Chaos Synchronization For a Financial Risk System”, Math. Comput. Simul., 154 (2018), 19–33        
7. Leonov G.A., “Generalized Lorenz Equations For Acoustic-Gravity Waves in the Atmosphere. Attractors Dimension, Convergence and Homoclinic Trajectories”, Commun. Pure Appl. Anal, 16:6 (2017), 2253–2267          
8. Zhang F., Liao X., Zhang G., “Some New Results For the Generalized Lorenz System”, Qual. Theor. Dyn. Syst., 16:3 (2017), 749–759          
9. Leonov G., “Hausdorff-Lebesgue Dimension of Attractors”, Int. J. Bifurcation Chaos, 27:10 (2017), 1750164          
10. Leonov G.A., “Lyapunov Dimension Formulas for Lorenz-Like Systems”, Int. J. Bifurcation Chaos, 26:14 (2016), 1650240            
11. Leonov G.A., Kuznetsov N.V., Korzhemanova N.A., Kusakin D.V., “Lyapunov dimension formula for the global attractor of the Lorenz system”, Commun. Nonlinear Sci. Numer. Simul., 41 (2016), 84–103          
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16. Leonov G.A., Mokaev T.N., “Lyapunov dimension formula for the attractor of the Glukhovsky–Dolzhansky system”, Dokl. Math., 93:1 (2016), 42–45            
17. Leonov G.A., Seledzhi S.M., “Lyapunov Dimension of Attractors of the Lorenz-Like Differential Equations”, Proceedings of the 3rd International Conference on Mathematics and Computers in Sciences and in Industry (Mcsi 2016), IEEE, 2016, 119–121      
18. Zhang F., Mu Ch., Zhou Sh., Zheng P., “New Results of the Ultimate Bound on the Trajectories of the Family of the Lorenz Systems”, Discrete Contin. Dyn. Syst.-Ser. B, 20:4 (2015), 1261–1276          
19. Nik H.S., Effati S., Saberi-Nadjafi J., “New Ultimate Bound Sets and Exponential Finite-Time Synchronization For the Complex Lorenz System”, J. Complex., 31:5 (2015), 715–730          
20. Zahedi M.Sh., Nik H.S., “Bounds of the Chaotic System For Couette-Taylor Flow and Its Application in Finite-Time Control”, Int. J. Bifurcation Chaos, 25:10 (2015), 1550133            
21. Leonov G.A., Kuznetsov N.V., Mokaev T.N., “Homoclinic Orbits, and Self-Excited and Hidden Attractors in a Lorenz-Like System Describing Convective Fluid Motion”, Eur. Phys. J.-Spec. Top., 224:8 (2015), 1421–1458        
22. Zhang F., Zhang G., Lin D., Sun X., “New Estimate the Bounds For the Generalized Lorenz System”, Math. Meth. Appl. Sci., 38:8 (2015), 1696–1704            
23. Leonov G.A., Alexeeva T.A., “Lyapunov Functions in Estimates of Attractor Dimensions For Generalized Rossler Systems”, Dokl. Math., 91:1 (2015), 5–8            
24. Zhang F., Mu Ch., Wang L., Wang X., Yao X., “Estimations for Ultimate Boundary of a New Hyperchaotic System and its Simulation”, Nonlinear Dyn., 75:3 (2014), 529–537            
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29. Nik H.S., Golchaman M., “Chaos Control of a Bounded 4D Chaotic System”, Neural Comput. Appl., 25:3-4 (2014), 683–692      
30. Wang P., Zhang Yu., Tan Sh., Wan L., “Explicit Ultimate Bound Sets of a New Hyperchaotic System and its Application in Estimating the Hausdorff Dimension”, Nonlinear Dyn., 74:1-2 (2013), 133–142            
31. Леонов Г.А., “Формулы ляпуновской размерности аттракторов обобщенной системы лоренца”, Доклады академии наук, 450:1 (2013), 13–13      ; Leonov G.A., “Formulas for the Lyapunov Dimension of Attractors of the Generalized Lorenz System”, Dokl. Math., 87:3 (2013), 264–268            
32. Леонов Г.А., “Функции Ляпунова в теории размерности аттракторов”, Прикладная математика и механика, 76:2 (2012), 180–196      ; Leonov G.A., “Lyapunov Functions in the Attractors Dimension Theory”, Pmm-J. Appl. Math. Mech., 76:2 (2012), 129–141          
33. Barreira L., Gelfert K., “Dimension estimates in smooth dynamics: a survey of recent results”, Ergodic Theory Dynam Systems, 31:3 (2011), 641–671            
34. Leonov G.A., Pogromsky A.Yu., Starkov K.E., “The dimension formula for the Lorenz attractor”, Phys Lett A, 375:8 (2011), 1179–1182              
35. Леонов Г.А., Райтманн Ф., Слепухин А.С., “Верхние оценки хаусдорфовой размерности отрицательно инвариантных множеств локальных коциклов”, Доклады Академии наук, 439:6 (2011), 736–739      ; Leonov G.A., Reitmann V., Slepukhin A.S., “Upper Estimates for the Hausdorff Dimension of Negatively Invariant Sets of Local Cocycles”, Doklady Mathematics, 84:1 (2011), 551–554        
36. Райтманн Ф., Слепухин А.С., “О верхних оценках размерности хаусдорфа отрицательно инвариантных множеств локальных коциклов”, Вестник Санкт-Петербургского университета. Серия 1: Математика. Механика. Астрономия, 2011, № 4, 61–70    
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38. Pogromsky A., Nijmeijer H., Rooda J., “A negative Bendixson-like criterion for a class of hybrid systems”, IEEE Trans. Automat. Control, 52:4 (2007), 586–595            
39. Morales C. A., Pacifico M. J., San Martin B., “Expanding Lorenz attractors through resonant double homoclinic loops”, SIAM J. Math. Anal., 36:6 (2005), 1836–1861 (electronic)            
40. Hirayama M., “An upper estimate of the Hausdorff dimension of stable sets”, Ergodic Theory Dynam. Systems, 24:4 (2004), 1109–1125          
41. Leonov G.A., “First-approximation instability criteria for non–stationary linearizations”, J. Appl. Math. Mech., 68:6 (2004), 827–838          
42. Gelfert K., “Maximum local Lyapunov dimension bounds the box dimension. Direct proof for invariant sets on Riemannian manifolds”, Z. Anal. Anwendungen, 22:3 (2003), 553–568          
43. М. И. Вишик, В. В. Чепыжов, “Колмогоровская $\varepsilon$-энтропия в задачах о глобальных аттракторах эволюционных уравнений математической физики”, Пробл. передачи информ., 39:1 (2003), 4–23      ; M. I. Vishik, V. V. Chepyzhov, “Kolmogorov $\varepsilon$-Entropy in Problems on Global Attractors of Evolution Equations of Mathematical Physics”, Problems Inform. Transmission, 39:1 (2003), 2–20  
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