American Institute of Mathematical Sciences

G. A. Leonov. Generalized Lorenz Equations for Acoustic-Gravity Waves in the Atmosphere. Attractors Dimension, Convergence and Homoclinic Trajectories. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2253-2267. doi: 10.3934/cpaa.2017111

Stefano Marò. Relativistic pendulum and invariant curves. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1139-1162. doi: 10.3934/dcds.2015.35.1139

Xingbo Liu, Deming Zhu. On the stability of homoclinic loops with higher dimension. Discrete and Continuous Dynamical Systems - B, 2012, 17 (3) : 915-932. doi: 10.3934/dcdsb.2012.17.915

Eleonora Catsigeras, Marcelo Cerminara, Heber Enrich. Simultaneous continuation of infinitely many sinks at homoclinic bifurcations. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 693-736. doi: 10.3934/dcds.2011.29.693

Pablo Aguirre, Bernd Krauskopf, Hinke M. Osinga. Global invariant manifolds near a Shilnikov homoclinic bifurcation. Journal of Computational Dynamics, 2014, 1 (1) : 1-38. doi: 10.3934/jcd.2014.1.1

Jordi-Lluís Figueras, Àlex Haro. A note on the fractalization of saddle invariant curves in quasiperiodic systems. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 1095-1107. doi: 10.3934/dcdss.2016043

Peng Huang, Xiong Li, Bin Liu. Invariant curves of smooth quasi-periodic mappings. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 131-154. doi: 10.3934/dcds.2018006

Michael L. Frankel, Victor Roytburd. Fractal dimension of attractors for a Stefan problem. Conference Publications, 2003, 2003 (Special) : 281-287. doi: 10.3934/proc.2003.2003.281

Sergey Gonchenko, Ivan Ovsyannikov. Homoclinic tangencies to resonant saddles and discrete Lorenz attractors. Discrete and Continuous Dynamical Systems - S, 2017, 10 (2) : 273-288. doi: 10.3934/dcdss.2017013

Enrique R. Pujals. On the density of hyperbolicity and homoclinic bifurcations for 3D-diffeomorphisms in attracting regions. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 179-226. doi: 10.3934/dcds.2006.16.179

Enrique R. Pujals. Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets. Discrete and Continuous Dynamical Systems, 2008, 20 (2) : 335-405. doi: 10.3934/dcds.2008.20.335

Alexandre Vidal. Periodic orbits of tritrophic slow-fast system and double homoclinic bifurcations. Conference Publications, 2007, 2007 (Special) : 1021-1030. doi: 10.3934/proc.2007.2007.1021

Xiao-Biao Lin, Changrong Zhu. Saddle-node bifurcations of multiple homoclinic solutions in ODES. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1435-1460. doi: 10.3934/dcdsb.2017069

Luis Barreira and Jorg Schmeling. Invariant sets with zero measure and full Hausdorff dimension. Electronic Research Announcements, 1997, 3: 114-118.

Katsutoshi Shinohara. On the index problem of $C^1$-generic wild homoclinic classes in dimension three. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 913-940. doi: 10.3934/dcds.2011.31.913

Cristina Lizana, Leonardo Mora. Lower bounds for the Hausdorff dimension of the geometric Lorenz attractor: The homoclinic case. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 699-709. doi: 10.3934/dcds.2008.22.699

V. Afraimovich, T.R. Young. Multipliers of homoclinic orbits on surfaces and characteristics of associated invariant sets. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 691-704. doi: 10.3934/dcds.2000.6.691

Isaac A. García, Jaume Giné. Non-algebraic invariant curves for polynomial planar vector fields. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 755-768. doi: 10.3934/dcds.2004.10.755

Peng Huang. Existence of invariant curves for degenerate almost periodic reversible mappings. Discrete and Continuous Dynamical Systems, 2022  doi: 10.3934/dcds.2022074

Lana Horvat Dmitrović. Box dimension and bifurcations of one-dimensional discrete dynamical systems. Discrete and Continuous Dynamical Systems, 2012, 32 (4) : 1287-1307. doi: 10.3934/dcds.2012.32.1287