
-
Previous Article
Accelerating planar Ornstein-Uhlenbeck diffusion with suitable drift
- DCDS Home
- This Issue
- Next Article
Recoding the classical Hénon-Devaney map
Universidade Federal de São Carlos, São Carlos, SP - 13565905, Brazil |
$ \begin{eqnarray*} f: \mathbb{R}^2\setminus \{y = 0\} &\rightarrow& \mathbb{R}^2 \\ (x,y) &\mapsto& \left(x+\dfrac{1}{y}, y-\dfrac{1}{y}-x\right) \end{eqnarray*} $ |
References:
[1] |
J. Aaronson, An Introduction to Infinite Ergodic Theory, Mathematical Surveys and Monographs, 50, American Mathematical Society, Providence, RI, 1997.
doi: 10.1090/surv/050. |
[2] |
R. L. Adler and B. Weiss,
The ergodic infinite measure preserving transformation of Boole, Israel J. Math., 16 (1973), 263-278.
doi: 10.1007/BF02756706. |
[3] |
P. Cirilo, Y. Lima and E. Pujals,
Ergodic properties of skew products in infinite measure, Israel J. Math., 214 (2016), 43-66.
doi: 10.1007/s11856-016-1344-3. |
[4] |
R. L. Devaney,
The baker transformation and a mapping associated to the restricted three-body problem, Commun. Math. Phys., 80 (1981), 465-476.
doi: 10.1007/BF01941657. |
[5] |
M. Hénon, Generating Families in the Restricted Three-Body Problem, Lecture Notes in Physics, New Series m: Monographs, 52, Springer-Verlag, Berlin, 1997.
doi: 10.1007/3-540-69650-4. |
[6] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977.
doi: 10.1007/BFb0092042. |
[7] |
M. Lenci,
On infinite-volume mixing, Comm. Math. Phys., 298 (2010), 485-514.
doi: 10.1007/s00220-010-1043-6. |
[8] |
S. Muñoz,
Robust transitivity of maps of the real line, Discrete Contin. Dyn. Syst., 35 (2015), 1163-1177.
doi: 10.3934/dcds.2015.35.1163. |
[9] |
S. Muñoz, Hyperbolicity and robust transitivity of non-compact invariant sets for the plane, preprint. |
[10] |
E. Pujals and F. Lenarduzzi, Generalized hénon-devaney maps, work in progress. |
[11] |
P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
show all references
References:
[1] |
J. Aaronson, An Introduction to Infinite Ergodic Theory, Mathematical Surveys and Monographs, 50, American Mathematical Society, Providence, RI, 1997.
doi: 10.1090/surv/050. |
[2] |
R. L. Adler and B. Weiss,
The ergodic infinite measure preserving transformation of Boole, Israel J. Math., 16 (1973), 263-278.
doi: 10.1007/BF02756706. |
[3] |
P. Cirilo, Y. Lima and E. Pujals,
Ergodic properties of skew products in infinite measure, Israel J. Math., 214 (2016), 43-66.
doi: 10.1007/s11856-016-1344-3. |
[4] |
R. L. Devaney,
The baker transformation and a mapping associated to the restricted three-body problem, Commun. Math. Phys., 80 (1981), 465-476.
doi: 10.1007/BF01941657. |
[5] |
M. Hénon, Generating Families in the Restricted Three-Body Problem, Lecture Notes in Physics, New Series m: Monographs, 52, Springer-Verlag, Berlin, 1997.
doi: 10.1007/3-540-69650-4. |
[6] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977.
doi: 10.1007/BFb0092042. |
[7] |
M. Lenci,
On infinite-volume mixing, Comm. Math. Phys., 298 (2010), 485-514.
doi: 10.1007/s00220-010-1043-6. |
[8] |
S. Muñoz,
Robust transitivity of maps of the real line, Discrete Contin. Dyn. Syst., 35 (2015), 1163-1177.
doi: 10.3934/dcds.2015.35.1163. |
[9] |
S. Muñoz, Hyperbolicity and robust transitivity of non-compact invariant sets for the plane, preprint. |
[10] |
E. Pujals and F. Lenarduzzi, Generalized hénon-devaney maps, work in progress. |
[11] |
P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |


Initial Point |
|
|
|
coordinates | |
|
|
coding | |
|
|
coordinates | |
|
|
coding | |
|
|
coordinates | |
|
|
coding | |
|
|
coordinates | |
|
|
coding | |
|
|
coordinates | |
|
|
coding | |
|
|
Initial Point |
|
|
|
coordinates | |
|
|
coding | |
|
|
coordinates | |
|
|
coding | |
|
|
coordinates | |
|
|
coding | |
|
|
coordinates | |
|
|
coding | |
|
|
coordinates | |
|
|
coding | |
|
|
[1] |
Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted three-body problem. Discrete and Continuous Dynamical Systems, 1995, 1 (4) : 463-474. doi: 10.3934/dcds.1995.1.463 |
[2] |
Jungsoo Kang. Some remarks on symmetric periodic orbits in the restricted three-body problem. Discrete and Continuous Dynamical Systems, 2014, 34 (12) : 5229-5245. doi: 10.3934/dcds.2014.34.5229 |
[3] |
Samuel R. Kaplan, Ernesto A. Lacomba, Jaume Llibre. Symbolic dynamics of the elliptic rectilinear restricted 3--body problem. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 541-555. doi: 10.3934/dcdss.2008.1.541 |
[4] |
Niraj Pathak, V. O. Thomas, Elbaz I. Abouelmagd. The perturbed photogravitational restricted three-body problem: Analysis of resonant periodic orbits. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 849-875. doi: 10.3934/dcdss.2019057 |
[5] |
Hadia H. Selim, Juan L. G. Guirao, Elbaz I. Abouelmagd. Libration points in the restricted three-body problem: Euler angles, existence and stability. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 703-710. doi: 10.3934/dcdss.2019044 |
[6] |
Qinglong Zhou, Yongchao Zhang. Analytic results for the linear stability of the equilibrium point in Robe's restricted elliptic three-body problem. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1763-1787. doi: 10.3934/dcds.2017074 |
[7] |
Mitsuru Shibayama. Non-integrability of the collinear three-body problem. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 299-312. doi: 10.3934/dcds.2011.30.299 |
[8] |
Jean-Baptiste Caillau, Bilel Daoud, Joseph Gergaud. Discrete and differential homotopy in circular restricted three-body control. Conference Publications, 2011, 2011 (Special) : 229-239. doi: 10.3934/proc.2011.2011.229 |
[9] |
Frederic Gabern, Àngel Jorba, Philippe Robutel. On the accuracy of restricted three-body models for the Trojan motion. Discrete and Continuous Dynamical Systems, 2004, 11 (4) : 843-854. doi: 10.3934/dcds.2004.11.843 |
[10] |
Edward Belbruno. Random walk in the three-body problem and applications. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 519-540. doi: 10.3934/dcdss.2008.1.519 |
[11] |
Richard Moeckel. A topological existence proof for the Schubart orbits in the collinear three-body problem. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 609-620. doi: 10.3934/dcdsb.2008.10.609 |
[12] |
Richard Moeckel. A proof of Saari's conjecture for the three-body problem in $\R^d$. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 631-646. doi: 10.3934/dcdss.2008.1.631 |
[13] |
Hiroshi Ozaki, Hiroshi Fukuda, Toshiaki Fujiwara. Determination of motion from orbit in the three-body problem. Conference Publications, 2011, 2011 (Special) : 1158-1166. doi: 10.3934/proc.2011.2011.1158 |
[14] |
Kuo-Chang Chen. On Chenciner-Montgomery's orbit in the three-body problem. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 85-90. doi: 10.3934/dcds.2001.7.85 |
[15] |
Marcel Guardia, Tere M. Seara, Pau Martín, Lara Sabbagh. Oscillatory orbits in the restricted elliptic planar three body problem. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 229-256. doi: 10.3934/dcds.2017009 |
[16] |
Ming Zhao, Cuiping Li, Jinliang Wang, Zhaosheng Feng. Bifurcation analysis of the three-dimensional Hénon map. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 625-645. doi: 10.3934/dcdss.2017031 |
[17] |
Regina Martínez, Carles Simó. On the stability of the Lagrangian homographic solutions in a curved three-body problem on $\mathbb{S}^2$. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1157-1175. doi: 10.3934/dcds.2013.33.1157 |
[18] |
Xiaojun Chang, Tiancheng Ouyang, Duokui Yan. Linear stability of the criss-cross orbit in the equal-mass three-body problem. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 5971-5991. doi: 10.3934/dcds.2016062 |
[19] |
Rongchang Liu, Jiangyuan Li, Duokui Yan. New periodic orbits in the planar equal-mass three-body problem. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 2187-2206. doi: 10.3934/dcds.2018090 |
[20] |
Abimael Bengochea, Manuel Falconi, Ernesto Pérez-Chavela. Horseshoe periodic orbits with one symmetry in the general planar three-body problem. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 987-1008. doi: 10.3934/dcds.2013.33.987 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]