國立高雄大學圖資館 |

Dynamical phase transitions in chaotic systems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Dynamical phase transitions in chaotic systemsby Edson Denis Leonel.
作者:	Leonel, Edson Denis.
出版者:	Singapore :Springer Nature Singapore :2023.
面頁冊數:	xvi, 74 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Chaotic behavior in systems.
電子資源:	https://doi.org/10.1007/978-981-99-2244-4
ISBN:	9789819922444$q(electronic bk.)

Dynamical phase transitions in chaotic systems
Leonel, Edson Denis.

Dynamical phase transitions in chaotic systems[electronic resource] /by Edson Denis Leonel. - Singapore :Springer Nature Singapore :2023. - xvi, 74 p. :ill., digital ;24 cm. - Nonlinear physical science,1867-8459. - Nonlinear physical science..

Posing the problems -- A Hamiltonian and a mapping -- A phenomenological description for chaotic diffusion -- A semi phenomenological description for chaotic diffusion -- A solution for the diffusion equation -- Characterization of a continuous phase transition in an area preserving map -- Scaling invariance for chaotic diffusion in a dissipative standard mapping -- Characterization of a transition from limited to unlimited diffusion -- Billiards with moving boundary -- Suppression of Fermi acceleration in oval billiard -- Suppressing the unlimited energy gain: evidences of a phase transition.

This book discusses some scaling properties and characterizes two-phase transitions for chaotic dynamics in nonlinear systems described by mappings. The chaotic dynamics is determined by the unpredictability of the time evolution of two very close initial conditions in the phase space. It yields in an exponential divergence from each other as time passes. The chaotic diffusion is investigated, leading to a scaling invariance, a characteristic of a continuous phase transition. Two different types of transitions are considered in the book. One of them considers a transition from integrability to non-integrability observed in a two-dimensional, nonlinear, and area-preserving mapping, hence a conservative dynamics, in the variables action and angle. The other transition considers too the dynamics given by the use of nonlinear mappings and describes a suppression of the unlimited chaotic diffusion for a dissipative standard mapping and an equivalent transition in the suppression of Fermi acceleration in time-dependent billiards. This book allows the readers to understand some of the applicability of scaling theory to phase transitions and other critical dynamics commonly observed in nonlinear systems. That includes a transition from integrability to non-integrability and a transition from limited to unlimited diffusion, and that may also be applied to diffusion in energy, hence in Fermi acceleration. The latter is a hot topic investigated in billiard dynamics that led to many important publications in the last few years. It is a good reference book for senior- or graduate-level students or researchers in dynamical systems and control engineering, mathematics, physics, mechanical and electrical engineering.

ISBN: 9789819922444$q(electronic bk.)

Standard No.: 10.1007/978-981-99-2244-4doiSubjects--Topical Terms:

182904
Chaotic behavior in systems.

LC Class. No.: Q172.5.C45

Dewey Class. No.: 003.857

Dynamical phase transitions in chaotic systems
LDR:03360nmm a2200337 a 4500 001 648921
003 DE-He213
005 20230713202238.0
006 m d
007 cr nn 008maaau
008 240116s2023 si s 0 eng d
020 $a 9789819922444$q(electronic bk.)
020 $a 9789819922437$q(paper)
024 7 $a 10.1007/978-981-99-2244-4 $2 doi
035 $a 978-981-99-2244-4
040 $a GP $c GP
041 0 $a eng
050 4 $a Q172.5.C45
072 7 $a GPFC $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a GPFC $2 thema
082 0 4 $a 003.857 $2 23
090 $a Q172.5.C45 $b L583 2023
100 1 $a Leonel, Edson Denis. $3 905631
245 1 0 $a Dynamical phase transitions in chaotic systems $h [electronic resource] / $c by Edson Denis Leonel.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2023.
300 $a xvi, 74 p. : $b ill., digital ; $c 24 cm.
490 1 $a Nonlinear physical science, $x 1867-8459
505 0 $a Posing the problems -- A Hamiltonian and a mapping -- A phenomenological description for chaotic diffusion -- A semi phenomenological description for chaotic diffusion -- A solution for the diffusion equation -- Characterization of a continuous phase transition in an area preserving map -- Scaling invariance for chaotic diffusion in a dissipative standard mapping -- Characterization of a transition from limited to unlimited diffusion -- Billiards with moving boundary -- Suppression of Fermi acceleration in oval billiard -- Suppressing the unlimited energy gain: evidences of a phase transition.
520 $a This book discusses some scaling properties and characterizes two-phase transitions for chaotic dynamics in nonlinear systems described by mappings. The chaotic dynamics is determined by the unpredictability of the time evolution of two very close initial conditions in the phase space. It yields in an exponential divergence from each other as time passes. The chaotic diffusion is investigated, leading to a scaling invariance, a characteristic of a continuous phase transition. Two different types of transitions are considered in the book. One of them considers a transition from integrability to non-integrability observed in a two-dimensional, nonlinear, and area-preserving mapping, hence a conservative dynamics, in the variables action and angle. The other transition considers too the dynamics given by the use of nonlinear mappings and describes a suppression of the unlimited chaotic diffusion for a dissipative standard mapping and an equivalent transition in the suppression of Fermi acceleration in time-dependent billiards. This book allows the readers to understand some of the applicability of scaling theory to phase transitions and other critical dynamics commonly observed in nonlinear systems. That includes a transition from integrability to non-integrability and a transition from limited to unlimited diffusion, and that may also be applied to diffusion in energy, hence in Fermi acceleration. The latter is a hot topic investigated in billiard dynamics that led to many important publications in the last few years. It is a good reference book for senior- or graduate-level students or researchers in dynamical systems and control engineering, mathematics, physics, mechanical and electrical engineering.
650 0 $a Chaotic behavior in systems. $3 182904
650 0 $a Phase transformations (Statistical physics) $3 225556
650 1 4 $a Dynamical Systems. $3 913342
650 2 4 $a Scale Invariance. $3 958810
650 2 4 $a Phase Transitions and Multiphase Systems. $3 402450
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Nonlinear physical science. $3 594745
856 4 0 $u https://doi.org/10.1007/978-981-99-2244-4
950 $a Physics and Astronomy (SpringerNature-11651)