. Ott, E., Sommerer, J. C., Antonsen Jr., T. M., & Venkataramani, S. Volume 450, Shlesinger, M. F., Zaslavsky, G. M., & Frisch, U., editors. Lecture Notes in Physics, pages 182-195. Springer Berlin Heidelberg, 1995. ![Lecture Notes in Physics [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex We consider a dynamical system that possesses a smooth manifold $M$ on which the dynamics is chaotic. This general situation occurs in spatially symmetric extended systems that exhibit chaotic behavior of a spatially symmetric pattern. (Motion on $M$ corresponds to spatial symmetry of the pattern.) Loss of stability transverse to $M$ has been called a blowout bifurcation and corresponds to spatial symmetry breaking. It is shown that a blowout bifurcation is typically associated with either one of two novel types of dynamical behavior: (a) ``on-off-intermittency'' (in which short bursts of motion far from $M$ occur between epoches where the orbit is exceedingly close to $M$), or (b) ``riddling'' of the basin of attraction of an attractor on (in which all points in the basin of the attractor on $M$ have arbitrarily nearby points in the basin of another attractor not on $M$).
@inbook{Shlesinger:1995gd,
Abstract = {We consider a dynamical system that possesses a smooth manifold $M$ on which the dynamics is chaotic. This general situation occurs in spatially symmetric extended systems that exhibit chaotic behavior of a spatially symmetric pattern. (Motion on $M$ corresponds to spatial symmetry of the pattern.) Loss of stability transverse to $M$ has been called a blowout bifurcation and corresponds to spatial symmetry breaking. It is shown that a blowout bifurcation is typically associated with either one of two novel types of dynamical behavior: (a) ``on-off-intermittency'' (in which short bursts of motion far from $M$ occur between epoches where the orbit is exceedingly close to $M$), or (b) ``riddling'' of the basin of attraction of an attractor on (in which all points in the basin of the attractor on $M$ have arbitrarily nearby points in the basin of another attractor not on $M$).},
Author = {Ott, Edward and Sommerer, John C. and {Antonsen Jr.}, Thomas M. and Venkataramani, Shankar},
Booktitle = {L{\'e}vy Flights and Related Topics in Physics},
Da = {1995/01/01},
Date-Added = {2014-11-09 07:34:04 +0000},
Date-Modified = {2014-12-05 07:21:08 +0000},
Doi = {10.1007/3-540-59222-9{\_}34},
Editor = {Shlesinger, Micheal F. and Zaslavsky, George M. and Frisch, Uriel},
Isbn = {978-3-540-59222-8},
La = {English},
Pages = {182-195},
Publisher = {Springer Berlin Heidelberg},
Se = {12},
Title = {Lecture Notes in Physics},
Title1 = {Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states},
Ty = {CHAP},
Url = {http://dx.doi.org/10.1007/3-540-59222-9_34},
Volume = {450},
Year = {1995},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/3-540-59222-9_34},
Bdsk-Url-2 = {http://dx.doi.org/10.1007/3-540-59222-9%7B%5C_%7D34}}
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It is shown that a blowout bifurcation is typically associated with either one of two novel types of dynamical behavior: (a) ``on-off-intermittency'' (in which short bursts of motion far from $M$ occur between epoches where the orbit is exceedingly close to $M$), or (b) ``riddling'' of the basin of attraction of an attractor on (in which all points in the basin of the attractor on $M$ have arbitrarily nearby points in the basin of another attractor not on $M$).","author":[{"propositions":[],"lastnames":["Ott"],"firstnames":["Edward"],"suffixes":[]},{"propositions":[],"lastnames":["Sommerer"],"firstnames":["John","C."],"suffixes":[]},{"propositions":[],"lastnames":["Antonsen Jr."],"firstnames":["Thomas","M."],"suffixes":[]},{"propositions":[],"lastnames":["Venkataramani"],"firstnames":["Shankar"],"suffixes":[]}],"booktitle":"Lévy Flights and Related Topics in Physics","da":"1995/01/01","date-added":"2014-11-09 07:34:04 +0000","date-modified":"2014-12-05 07:21:08 +0000","doi":"10.1007/3-540-59222-9_34","editor":[{"propositions":[],"lastnames":["Shlesinger"],"firstnames":["Micheal","F."],"suffixes":[]},{"propositions":[],"lastnames":["Zaslavsky"],"firstnames":["George","M."],"suffixes":[]},{"propositions":[],"lastnames":["Frisch"],"firstnames":["Uriel"],"suffixes":[]}],"isbn":"978-3-540-59222-8","la":"English","pages":"182-195","publisher":"Springer Berlin Heidelberg","se":"12","title":"Lecture Notes in Physics","title1":"Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states","ty":"CHAP","url":"http://dx.doi.org/10.1007/3-540-59222-9_34","volume":"450","year":"1995","bdsk-url-1":"http://dx.doi.org/10.1007/3-540-59222-9_34","bdsk-url-2":"http://dx.doi.org/10.1007/3-540-59222-9%7B%5C_%7D34","bibtex":"@inbook{Shlesinger:1995gd,\n\tAbstract = {We consider a dynamical system that possesses a smooth manifold $M$ on which the dynamics is chaotic. 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